{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Design of Digital Audio IIR Filters\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de) or main author of this notebook [Frank Schultz](mailto:frank.schultz@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Typical 1st & 2nd Order IIR-Filters in Audio Signal Processing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preliminaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We often use standard LaTex-style citing within the text. At the moment there is no commonly accepted long-term solution for rendering a reference bib-list in a Jupyter notebook automatically, so we leave the bibtex information here as plain text as well. However, it is working with enabled `LaTeX environments for Jupyter` of the `Nbextensions` using the external `biblio.bib` file in the `jupyter notebook` environment. Otherwise, digital resources appear linked with their URLs and you might check [biblio.bib](biblio.bib) manually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import signal\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import functions for filter coefficients calculation and plotting from accompanying [audiofilter.py](audiofilter.py) next."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import audiofilter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to print filter coefficients in high precision. This is useful when e.g. working with fixed point number representation and checking whether its resolution fits for the filter coefficients' dynamic range. So we set up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(floatmode=\"unique\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We define the (typical audio) sampling frequency in Hz as constant throughout this notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "fs = 48000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction\n",
    "\n",
    "We recollect common **1st** and **2nd** order infinite impulse response (IIR) **audio filters** as analog **Laplace domain** transfer functions. \n",
    "\n",
    "We derive their transfer function counterparts in z-domain as **bilinear transforms**, applying **prewarping** for cut/mid frequency and for quality/bandwidth.\n",
    "\n",
    "If you are interested in a Matlab based implementation of these filters, please have a look at the TU Berlin project [AKTools](https://www.ak.tu-berlin.de/menue/publications/open_research_tools/aktools/), cf. [Fabian Brinkmann, Stefan Weinzierl: \"AKtools -- An Open Software Toolbox for Signal Acquisition, Processing, and Inspection in Acoustics.\" In: *142nd AES Convention, Berlin, Germany, 2017*, e-Brief 309.](http://www.aes.org/e-lib/browse.cfm?elib=18685)\n",
    "\n",
    "Although more sophisticated filter designs exist, the discussed filter characteristics solve many IIR based audio filtering tasks, such as in a typical [digital audio workstation](https://en.wikipedia.org/wiki/Digital_audio_workstation) (DAW) and available [plugins](https://plugins.iem.at/), in digital mixing consoles, loudspeaker management systems, power amplifiers with DSP capabilities, audio player software and home entertainment systems. \n",
    "\n",
    "Higher order IIR filters can be built from second order filters. A series connection of the discussed filter types achieves more complex transfer functions often being used in the mentioned applications. A so called graphical equalizer is a prominent example for that, which is however not restricted to build from series connection.\n",
    "As another application, a [Shelving Filter Cascade with Adjustable Transition Slope and Bandwidth](http://www.aes.org/e-lib/browse.cfm?elib=20756) was a recent project by the authors, whose [open source code](https://github.com/spatialaudio/aes148-shelving-filter) might merged into here as well sometime. \n",
    "\n",
    "A brilliant, open access review on digital audio filter design is \\cite{ValimakiReiss2016} [Vesa Välimäki, Joshua D. Reiss (2016): \"All About Audio Equalization: Solutions and Frontiers.\"\n",
    "In: *Appl. Sci.*, **6**(5), 129, https://doi.org/10.3390/app6050129](https://doi.org/10.3390/app6050129). The filters derived there in Sec. 3 are consistent with our later called **type III** filters.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Standardized vs. Non-Standardized Filter Characteristics\n",
    "For the **standardized** lowpass, highpass, bandpass, bandstop and allpass filters, the Laplace transfer functions and their coefficients are well known from literature e.g. \\cite{Moschytz1981}, [\\cite{TietzeSchenk2008}](http://www.tietze-schenk.de/).\n",
    "\n",
    "For shelving and parametric filters **no standardization w.r.t. the pole/zero qualities and cut-frequencies and thus positions of poles and zeros** exists. Based on \\cite{Zoelzer2002,Zoelzer2005},[\\cite{Zoelzer2008}](https://link.springer.com/chapter/10.1007/978-3-540-34301-1_15),[\\cite{Zoelzer2011}](https://doi.org/10.1002/9781119991298) (in which these filters are derived with the help of allpass filters) and some other articles \\cite{Kimball1938}, \\cite{Bristow-Johnson}, [\\cite{Bristow-Johnson1994}](http://www.aes.org/e-lib/browse.cfm?elib=6326), [\\cite{Orfanidis1997}](http://www.aes.org/e-lib/browse.cfm?elib=7854), [\\cite{Christensen2003}](http://www.aes.org/e-lib/browse.cfm?elib=12429) widely used approaches can be found.\n",
    "\n",
    "\\cite{Christensen2003} discusses the generalized form of the biquad transfer function for progammable filters.\n",
    "\n",
    "Three characteristics (labeled as types **I, II and III**) are most prominent, leading to different transfer functions for the same parameter set. This regularly leads to misconceptions. In 2016 the Audio Engineering Society (AES) readdressed this [issue at 141st AES Convention in Los Angeles](http://www.aes.org/events/141/workshops/?ID=5197)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Overview of Filter Transfer Functions\n",
    "\n",
    "The following filter characteristics are discussed in this notebook:\n",
    "\n",
    "[1st order lowpass](#lowpass1st)\n",
    "\n",
    "[2nd order lowpass](#lowpass2nd)\n",
    "\n",
    "[1st order highpass](#highpass1st) \n",
    "\n",
    "[2nd order highpass](#highpass2nd)\n",
    "\n",
    "[2nd order bandpass](#bandpass2nd) \n",
    "\n",
    "[2nd order bandstop](#bandstop2nd)\n",
    "\n",
    "[1st order allpass](#allpass1st) \n",
    "\n",
    "[2nd order allpass](#allpass2nd)\n",
    "\n",
    "[2nd order PEQ](#peq2nd) type **I,I,III**\n",
    "\n",
    "[1st order low-shelving](#lowshv1st) type **I,I,III**\n",
    "\n",
    "[2nd order low-shelving](#lowshv2nd) type **I,I,III**\n",
    "\n",
    "[1st order high-shelving](#highshv1st) type **I,I,III**\n",
    "\n",
    "[2nd order low-shelving](#highshv2nd) type **I,I,III**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bilinear Transform of an IIR Biquad\n",
    "\n",
    "The transformation of the analog filter prototypes (given as Laplace transfer function) towards the digital prototype (given as z-domain transfer function) is here performed with the [bilinear transform](bilinear_transform.ipynb) \\cite[Ch. 7.1.2]{OppenheimSchaferBuck2004}) applying frequency and bandwidth prewarping techniques.\n",
    "\n",
    "There are other approaches such as the impulse invariant method, the matched z-transform method and higher order Taylor series truncations \\cite{Clark2000}, \\cite{Gunness2007}, \\cite{Alaoui2007}, \\cite{Schmidt2010}, \\cite{Alaoui2010} that yield higher precision matching of the analog and digital transform. For didactical purpose we restrict ourselves to the bilinear transform of IIR biquads, which is widely used in practice as well.\n",
    "\n",
    "Once the idea is set, it is comparably easy to adapt other digital filter design methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us define the angular frequency $\\omega$ in rad/s, $\\mathrm{i}^2=-1$ and the sampling frequency $f_s$ in Hz. The connection between the Laplace domain and the z-domain is then given by\n",
    "\n",
    "\\begin{equation}\n",
    "s = \\mathrm{i}\\,\\omega \\qquad z = \\mathrm{e}^{\\frac{s}{f_s}} \\qquad \\stackrel{\\text{linearization from Taylor series}}{\\rightarrow} \\qquad s = 2\\,f_s\\,\\frac{z-1}{z+1}.\n",
    "\\end{equation}\n",
    "\n",
    "The continuous and discrete-time transfer functions $H(s)$ and $H(z)$, respectively for the 2nd order filter (biquad) are given as \n",
    "\n",
    "\\begin{equation}\n",
    "H(s) = \\frac{B_0\\,s^2+B_1\\,s+B_2}{A_0\\,s^2+A_1\\,s+A_2}\n",
    "\\qquad\n",
    "H(z) = \\frac{b_0+b_1\\,z^{-1}+b_2\\,z^{-2}}{1+a_1\\,z^{-1}+a_2\\,z^{-2}}\n",
    "\\end{equation}\n",
    "\n",
    "following typical conventions for the denotation of the filter coefficients $A$, $B$, $a$, $b$ (Python and Matlab compatible)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bilinear transform rule $s = 2\\,f_s\\,\\frac{z-1}{z+1}$ can be inserted to $H(s)$ and the result can be brought to form of biquad given as $H(z)$ above. Then the coefficients for the biquad are generally given by, cf. [bilinear transform](bilinear_transform.ipynb)\n",
    "\n",
    "\\begin{align}\n",
    "b_0 &= \\frac{B_2+2\\,B_1\\,f_s+4\\,B_0\\,f_s^2}{A_2+2\\,A_1\\,f_s+4\\,A_0\\,f_s^2}\\newline\n",
    "b_1 &= \\frac{2\\,B_2-8\\,B_0\\,f_s^2}{A_2+2\\,A_1\\,f_s+4\\,A_0\\,f_s^2}\\newline\n",
    "b_2 &= \\frac{B_2-2\\,B_1\\,f_s+4\\,B_0\\,f_s^2}{A_2+2\\,A_1\\,f_s+4\\,A_0\\,f_s^2}\\newline\n",
    "a_1 &= \\frac{2\\,A_2-8\\,A_0\\,f_s^2}{A_2+2\\,A_1\\,f_s+4\\,A_0\\,f_s^2}\\newline\n",
    "a_2 &= \\frac{A_2-2\\,A_1\\,f_s+4\\,A_0\\,f_s^2}{A_2+2\\,A_1\\,f_s+4\\,A_0\\,f_s^2}.\n",
    "\\end{align}\n",
    "\n",
    "The function `audiofilter.bilinear_biquad(B, A, fs)` realizes the bilinear transformation based on the above given equations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frequency and Bandwidth Prewarping\n",
    "\n",
    "A so called prewarping \\cite[eq. (7.28)]{OppenheimSchaferBuck2004} of the cut/mid frequency $f_c$/$f_m$ in Hz\n",
    "\n",
    "\\begin{equation}\n",
    "\\omega_{c} \\Leftarrow 2\\,f_s\\,\\tan{\\left(\\pi\\frac{f_{c}}{f_s}\\right)}\n",
    "\\qquad\n",
    "\\omega_{m} \\Leftarrow 2\\,f_s\\,\\tan{\\left(\\pi\\frac{f_{m}}{f_s}\\right)}\n",
    "\\end{equation}\n",
    "\n",
    "is realized in the function `audiofilter.f_prewarping(f, fs)`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The connection between the bandwidth $BW_\\text{oct}$ in octaves and the corresponding bandpass-related quality $Q_\\text{BP}$ is given as\n",
    "\n",
    "\\begin{equation}\n",
    "BW_\\text{oct} = \\frac{2}{\\log_\\mathrm{e}(2)}\\,\\sinh^{-1}(\\frac{1}{2\\,Q_\\text{BP}})\n",
    "\\qquad\n",
    "Q_\\text{BP} = \\frac{1}{2\\,\\sinh(\\frac{\\log_\\mathrm{e}(2)}{2}\\,BW_\\text{oct})}\n",
    "\\end{equation}\n",
    "\n",
    "with the natural logarithm $\\log_\\mathrm{e}(\\cdot)$ and the hyperbolic sine $\\sinh(\\cdot)$. The functions `bw_from_q()` and `q_from_bw()` do this job."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prewarping of the bandpass quality for the parametric, bandpass and bandstop filters can be done with\n",
    "\n",
    "* **tan**-prewarping, cf. [\\cite{Clark2000}](http://www.aes.org/e-lib/browse.cfm?elib=12069)\n",
    "\n",
    "\\begin{equation}\n",
    "Q_\\text{BP} \\Leftarrow \\frac{\\frac{\\pi\\,f_m}{f_s}}{\\tan\\left(\\frac{\\pi\\,f_m}{f_s}\\right)} Q_\\text{BP}\n",
    "\\end{equation}\n",
    "\n",
    "* **cos**-prewarping, cf. \\cite{Thaden1997} **(default)**\n",
    "\n",
    "\\begin{equation}\n",
    "Q_\\text{BP} \\Leftarrow \\cos(\\pi\\,\\frac{f_m}{f_s}) Q_\\text{BP}\n",
    "\\end{equation}\n",
    "\n",
    "* **sin**-prewarping of the bandwidth in octaves, cf. \\cite{Bristow-Johnson1994}\n",
    "\n",
    "\\begin{equation}\n",
    "BW_\\text{oct} \\Leftarrow \\frac{2\\,\\pi\\,\\frac{f_m}{f_s}}{\\sin(2\\,\\pi\\,\\frac{f_m}{f_s})} BW_\\text{oct}\n",
    "\\end{equation}\n",
    "\n",
    "exhibiting slightly different characteristics. The function `audiofilter.q_prewarping(q, fm, fs, q_warp_method=\"cos\")` handles the discussed cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting Routine\n",
    "We here establish a plotting routine for the `bode_plot()`, i.e. the magnitude and phase spectrum of the filter's transfer function. For that we use the `freqs()` and `freqz()` functions implemented in the `signal` package. We also use the self-implemented `audiofilter.zplane_plot()` function for plotting zeros and poles in the z-plane. Furthermore, we utilize a `magnitude_plot()`function for overlaying several magnitude plots for convenient comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bode_plot(B, A, b, a):\n",
    "    fig = plt.figure(figsize=(10, 6.25))\n",
    "    audiofilter.bode_plot(B, A, b, a, fs=fs, N=2**12, fig=fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def magnitude_plot(x, y, title, legend):\n",
    "    fig = plt.figure(figsize=(6, 3))\n",
    "    audiofilter.magnitude_plot_overlay(x, y, title, legend, fig=fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial Example\n",
    "\n",
    "#### Without Frequency Prewarping\n",
    "This initial example demonstrates the application of the bilinear transform and the plotting routine, here **without frequency prewarping**. We use a lowpass filter (simplest RC circuit) with the cut frequency $f_c$ in Hz, which is linked to $\\omega_c=2\\,\\pi\\,f_c=\\frac{1}{R\\,C}$. For the discrete-time filter we need to specify the sampling frequency $f_s$ in Hz. We already have done this at the beginning of this notebook.\n",
    "\n",
    "First, define the cut frequency in Hz for the lowpass filter, i.e. the frequency where the magnitude is -3.01 dB and the phase is -45 deg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "fc = 10000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need this as angular frequency in rad/s, thus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "wc = 2 * np.pi * fc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define the filter coefficients in s-domain. Actually, we only need two $B$ and two $A$ coefficients, since the RC circuit is a 1st-order filter. For consistency with later ideas we adapt to a 2nd-order structure by filling with preceding zeros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.array([0.0, 0, 1])\n",
    "A = np.array([0, 1 / wc, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, the discrete-time filter is obtained by the bilinear transform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "b, a = audiofilter.bilinear_biquad(B, A, fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We check, if our implementation is equivalent with that of the `signal` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "bsignal, asignal = signal.bilinear(B, A, fs)\n",
    "np.testing.assert_allclose(b, bsignal)  # check if equivalent\n",
    "np.testing.assert_allclose(a, asignal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If no exception occured, nicely done so far.\n",
    "\n",
    "Now we are able to plot the continuous-time (s-domain) and discrete-time (z-domain) filters. If we do this for analog frequency values we can overlay the plots for comparison. Furthermore, we depict the zeros and poles in the zplane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [0. 0. 1.]\n",
      "A = [0.0000000000000000e+00 1.5915494309189534e-05 1.0000000000000000e+00]\n",
      "b = [0.3955872317588232 0.7911744635176464 0.3955872317588232]\n",
      "a = [ 1.                   0.7911744635176464  -0.20882553648235358]\n"
     ]
    },
    {
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   "source": [
    "bode_plot(B, A, b, a)"
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   "source": [
    "#### With Frequency Prewarping\n",
    "\n",
    "In the above example you see that the digital filter (z-domain, red) deviates from its analog (s-domain, blue) counterpart for frequencies near half of the sampling frequency. This deviation can be precisely resolved for one frequency. Performing such a matching is known as frequency prewarping. Typically, the -3.01 dB / -45 deg cut frequency is chosen for such frequency prewarping, but we are free to choose any other frequency if it fits our application.\n",
    "\n",
    "Now then, we do the same procedure **with frequency prewarping**, in order that the intended analog $f_c$ matches the 'digital' $f_c$ in discrete-time domain.\n",
    "\n",
    "$B$, $A$, $f_c$ and $\\omega_c$ (`B`, `A`, `fc`, `wc`) remain unchanged. We use the `prewarping_f()` function on the cut frequency `fc` as"
   ]
  },
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   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "wc= 10000.0\n",
      "wcpre= 11723.89277804802\n"
     ]
    }
   ],
   "source": [
    "wcpre = audiofilter.f_prewarping(fc, fs)\n",
    "print(\"wc=\", wc / 2 / np.pi)\n",
    "print(\"wcpre=\", wcpre / 2 / np.pi)"
   ]
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   "metadata": {},
   "source": [
    "In the calulation of `A` and `B` every dependence of `wc` is to be exchanged with `wcpre`, leading to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "Bpre = B\n",
    "Apre = np.array([0, 1 / wcpre, 1])"
   ]
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   "source": [
    "The bilinear transform of these coefficients yields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "b, a = audiofilter.bilinear_biquad(Bpre, Apre, fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot our results, which indicate that analog and digital transfer function matches exactly in the low frequency region and precisely the -3.01 dB point at $f_c$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [0. 0. 1.]\n",
      "A = [0.0000000000000000e+00 1.5915494309189534e-05 1.0000000000000000e+00]\n",
      "b = [0.4341737512063021 0.8683475024126042 0.4341737512063021]\n",
      "a = [ 1.                   0.8683475024126042  -0.13165249758739586]\n"
     ]
    },
    {
     "data": {
      "application/pdf": 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    "bode_plot(B, A, b, a)"
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   "source": [
    "Take a moment to check the differences in filter coefficients $a$ and $b$ of the filter versions **with frequency prewarping** vs. **without frequency prewarping**. These differences become more subtle for $f_c\\ll f_s/2$."
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   "source": [
    "### Definition of 1st / 2nd Order Filter Transfer Functions\n",
    "\n",
    "In [audiofilter.py](audiofilter.py) we implemented functions to calculate filter coefficients of lowpass, highpass, allpass, bandpass, bandstop, shelving and parametric filters. These characteristics are very often used in audio applications, cf. e.g. [\\cite{TietzeSchenk2008}](http://www.tietze-schenk.de/), \\cite{Moschytz1981}, \\cite{Christensen2003}, \\cite{Zoelzer2008}, \\cite{Zoelzer2011}, \\cite{Bristow-Johnson1994}, \\cite{Redmon2013}, \\cite{ValimakiReiss2016}."
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    "<a id=\"lowpass1st\"></a>\n",
    "### 1st Order Lowpass `lp1st`\n",
    "\n",
    "\\cite{TietzeSchenk2008}, \\cite{Moschytz1981}\n",
    "\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| 0 | 0 | 1 | 0 | $\\frac{1}{\\omega_\\text{c}}$ | 1 |\n",
    "\n",
    "with cut frequency $\\omega_c=2\\pi f_c$ in rad/s"
   ]
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   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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     "text": [
      "B = [0. 0. 1.]\n",
      "A = [0.0000000000000000e+00 1.5915494309189535e-04 1.0000000000000000e+00]\n",
      "b = [0.061511768503621556 0.12302353700724311  0.061511768503621556]\n",
      "a = [ 1.                   0.12302353700724311 -0.8769764629927569 ]\n"
     ]
    },
    {
     "data": {
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   "source": [
    "fc = 1000  # Hz\n",
    "B, A, b, a = audiofilter.biquad_lp1st(fc, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
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    "<a id=\"lowpass2nd\"></a>\n",
    "### 2nd Order Lowpass `lp2nd`\n",
    "\n",
    "\\cite{TietzeSchenk2008}, \\cite{Moschytz1981}\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| 0 | 0 | 1 | $\\frac{\\text{b}_\\text{i}}{\\omega_\\text{c}^2}$ | $\\frac{\\text{a}_\\text{i}}{\\omega_\\text{c}}$ | 1 |\n",
    "\n",
    "with cut frequency $\\omega_c=2 \\pi f_c$ in rad/s and filter characteristic coefficients $\\text{b}_\\text{i}$ and $\\text{a}_\\text{i}$ (see Appendix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [0. 0. 1.]\n",
      "A = [2.5330295910584447e-08 2.2507907903927655e-04 1.0000000000000000e+00]\n",
      "b = [0.0039161266605473675 0.007832253321094735  0.0039161266605473675]\n",
      "a = [ 1.                 -1.815341082704568   0.8310055893467575]\n"
     ]
    },
    {
     "data": {
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jCLdceSPvxFywnTGXPI/DnE2Mszc/wpnzaKP1t7x5I+/EXLCdMZc8r+7Q/dmNa8zT/Jyk/+SQmKXNx97LhvQa2xl1yfNA1LPuCgq0sFxUFNCY0g05dcUEwugz3jOdeJCTuusVDbiQ8//lpVz2Nvu8cLDl+69e6XMW+7tq3XuuQqB5DpfnQA231nnu2Tmm57NvvCtHexOQC5x2g+rQTJVKrYFyQh9dbAq5HJcuJQUUQgrHs+wDTzDqqOoJWz6UDXQil+HeWpXLCVtteAxWGc+XQmli0JWPhUAuxcDXQuvwuZyC1wDNeusz+Cie4OWZV9Idm2kNU8tUHAMMoR64hmVkKCzfq3hwGNpR+AByHpRmwjfPiqMJtaiAhyU5IIf2KwSDORJCniFnZMhU3oFJvaouXJJeKhiEYIec0R8GMQ3JEV2QogGWCGyzDfWAsI4OqsLhgKcHI0RVtQ4DT08rhUZyS1zzHMhQD5eH4G1MA3P6fJ7qJJSkcgs7GRLAttbYevSbJ0QDawgkQ+XNoTDJEVITpgEeGT3D08k8sI3JXFZo4xDAW9laQcIAu2iTc3aANkRTT5WLU9yAIarA48n1EDd61KN9oZxwNqac1daEXKNdnLJCQ+p5Yha+NCmh1Z4uMIR60NzwhDUMnrNLGGGYah0APh3Am8YS0UuqcEbshJdzq87zhYC3ksvJnZTsgN52Ea8pTHhUM6Nz8gCFVzw0TSp+aQ360A0Oug9nVs9dex6q08mGAT9jonyuB8NZsAHQmwEKhhelWhoC3VtOxuCNwDqjJeXpyJgWWgLemuf5dalLwBP3MZf+cNBqY6oF8VQr59M8vJ15mt+WI/myQEMeLQ/bh8vkRd2GPS7lfZRtqH4ERrjmR0oLbjsSq4sHWDqSlKuBLh2Jc3nVkYRQq4QsHEmyxuUVRwLrqla0cCQweu1XHInVfOS2I0kwerPiSOAo3IojycUgVxwJmlYrPfSOBJ1YC0z0jsQnX626dyQ8CWhvOxKWDzhXqRCOJOlsVxyJp3oXMswJbwr0IzbnVOVnphlTujPXRozVuhS6oB+BLHgD/QjwdKU+Bf2IT3AkxY8kxdopkyNxCtZkiyPBmFGrO0BNNEwImNCRAJCpeERiFRUHu6UjgeP2dvIk6HP0Cz2Jw/BXvRHP+sPmYERcqMrBVFNF/0PXUtA0ErjH5KuHOReOcBmdb1P1RjRE1pwI9CTQUF2rUghPEsaka7mR4klChgrRkzieQtSTJ3HZs1d5Bhwj1ORJABR8JHw1XAYabWpNhsjMZWNycRkRQLmCSMxjMtok3mk9wlVOiMDHB3CO9AEu61CKQ0jXkKC8HoPoZfLDCzdsH0l7aPLlQ9apHxZFH1y0wUTY6LxNYdT5xPCiaMP3Xz1/84CCDSHI2fFKwYZG7go2NLIotkDi7YINHCBWCjawLs1KwQa6iNsFG/Rco0I2bSa+kHLM1BsOF7WOQiMGt/ImSUyNp7stwk1HncVtL5pxWUP28Qo2hIZK0u2M4Ar1PsfTc5Cn06vrbzMpdWH69Pw8uzElJGlney/VKPhyfZZ0c+ks9YXp03Si/fbB9ceuE3H5m18rRXwwlSIQdMHHTu2/ezb97mUihBkGv2aGwe83Q8Q1/2/M8AHVKXZY4a/1KX6tT3FUfYr7+KOHFqewnpOsMqXAVDhzlsMihwC1BriNeNOIcAMsJJdLlUDBoaPPJSraA/zTOJZZ92JJYPFxXhtwJ65AS286uT5J+mTxxOnkEiFjsTJ4Cc/lDEydy4wBExynnaR6Nh5TGkw8uQWJ8M6aiMkcZuTJsZZiOUIeUwqMxjzLc2VE3fA/ngX2osMjiLIwpwmOpQMwT82c1ydJhaFMlbvBQpAxF8JcOJXVqZmxCZzBKZW7ZrCqP2v42cKjNZpVJDEL1BHNOItnMYeFISRMvQUUgvri5DwD0FiKEoinTUIEaXLUki+mk5gfO2cXrbCJRc0wyfWyzaxgBsYaM3Uhn6QKMARZICcYC5RFM7o+EY0WPSgEFL29rhlTlP2+tNacuq2Zbt8EryyhQEzu9rHBEMeYFAy8M0pB7iztQQcHN1knGNHZ4oEFrEwGFpa7ljY7G3JC3wdMhAokBZYSXYi9l1t+GDPP2bmdbm1YLJ3Z61ffvn0j9yiO7BNnuFDNFT6JW6Pu7pEtxnf3h9N25NHu4FUy4aH9gbnzL7Y/mgF3uAk3t7tHNlmv9ElfTSjC5+hQymTi8b5XKvDdRvuRQHrHbQ2YdB8BCPJuILdZbwHpLWsdq7LqqFdx9B8Mjiyd7JOPrhe2kffjuMl6E8fMgBFjZrZJmRUg9Sh2w5t34fJ5qFqMB+H7l94FPgU9Gdw0Y1idVv7tQmQsZnd/PQf0mCDLSYPg8r+7t7o//eLH59/89PbHD8V1iYiZ1VmU4/aoiLkb8YFj+zpfXlwSl+TVsV2zJLmaUBkyl/5j0CkpHe81tv9iB3eBnDZutCYk1U2DBHV3n3ScRaf0vLd6RRsueGc4keS1uc8QH3+xY7wED6y1y9qYrlsadX+3SM6yWzrem93i4FJ92QJW6n6R19+FtSTNMvGYDnTd0qj7u0Vylt3S8d7slpi4S+/RNDi++3SL+XuwljazFr3SiLs7RfIVfdJxXok+4N3GnPy5U4wK8t4wNaoPJhiWsnLbXQcVurFZUPejKDlLGDve98CRx3J11rzqJYdOfz80LAOzinj5TIdlo+7HUnKWWHa874FlcGNw2ivmAJrORX9oWPLWFChJ7kZCQd2PpeQssex43wPLbEcXLBcNma0po5APDEs2XCXLm3cEloK6G8uOs8Cy572NpeUhtxS0xbwx2S7QXmQuW21GTJenTb960XuXxJx5r5PcO/iwZmn/co1Zmj7nx09q0u0eLBIJxfRajnskG50jl+J1GJ1XseT6eVZVUtaZep+6yk5FO9G1VpFXZJnItA9dcgl9Dsyos+U+HC7iTdN3z9uSyp1LNoFhiOU+HA+bshnMeS+Xozm6kqHnWYRCZ8Mlecd7wizTx0DnDcTJRBb49bwQ2Kpy35jnRUsp+8jtBXRMQo/kQncj4iQb6hK+RuNNpSPcgtZgqsGsMIxNpkoVmefM69bKnUsJMNTnY83dxoyR6WKOLqCQebQna3Ybe9HW9DhPL52tQoxteNmUjiaZQncjJNOUKpvR6in5DnEcnufMp9xIZRjaFXSoJyop3iSVM6Wt4JQ83Ugy79KyTIksjWSOqFGemxSIRQLMpiQwesfczZwcdz14aRzELXQbR6e5s1CsDDF+rF1o8TwmyKbunSigVi6k8uhnTJvhMsvFtFbFmj/uDW+uw58MOuYLCGKrWNAjQA+bKvfpAqVQmqlh6snABRQ3EABoWTryTDQLkzuxYwqxZms6ig59DXRh6BOLXnCF7pgTGChWuT0i1nRDOGdeHsY0P9Kzc8Ct0NsaqnRXLhIGGv7ieV48FVLOfsE/lD3gxE2krj0sxBuLo5WtZ66TD5bbVlJaR7VWJmjXgeNoBSZ7JipLLDHoMyWWRVkk9I6HstFIFmOVXcU9o2gML07rutaZcldapExSFRzepXTJs+tUx+maoJ0WquYUMznLRVtSM50qad4xhV6RnWL6QvRqofgWTgTPE4TOUGwuib5+YVe8mAkuHGNGZ4W23LIGl+d7o+UdU9Di4rqkkVteJAee0fROgRcWJYwBxVkIJ2Ij9JgHm1zvdGxkDnLm3l3npGwst8TZmHunZqFQCG71tDM6O0FbbpHHb23vMklX0LrsehfL22PxrloAVLhk7nYxbLYLFy52weSURj7OG//wObqePa+sgyNzJvbN0eifFKNVtm8+kwWtOu+gN3G594kWxHI8RcCjWXsRfeN8DydPkoFjDgv4mbgd8Ntg+u5iXTGvdM0GF93L3VU8HaPu1WG6vNFUuZr68BJEjGiuPt+0TfPkAaYwC91kXnvwfiLPqgz/jgm4MuXkgVB9bVhLA+gsTIV339jz4R1hWRp+IUSbfW+IcBUjhkZf8pGF4ZZsffSVXRg6U/SB0uS8mmPQeJPW3E7uHQlT7nnCqDqM2e8w497gRSWjX7gpZtwbzkl879W0KvCVXHThBDP55args8fM1O4cixoI98rbGdlNoffGIGOQmxxXc96ZgFobFr5eLg6LoaF7uo0kHe828MiWiHFKtlsMa1JGMQhKRMSY2QEoxtgOcDEmd/0jxvCuP8WY3/W/iBE6fRExRadfIgSR6igilk57RYTTabuIiDrrEAGUNCYRbknTE9FZZ6kimussW0R/nScQ0WLnOUR02XkaEY12nklEr50nm2Pdzu+JyLjzkyKS7vyqiLw7Pywjdem3L9Gnqd6jTzr25WmvDk6v2ehnH/k6N5UpocztEr8oF4JOC3dQsQgDjFaQOTYBF54pIzFgRC/JOlxQcrks2vG25MTbg5mtozAiapMKmccR+SwPOE1vw0waKloKAzZql+4jyDAodEfQg2CLWCxoU6q6tyYw14HAOXIQDdZMW2SxhkHKBqs9yyaQOxPJIYywyzKZEM/yxlZN4Tu2nudkNKO4vhFcNSpXuooWB7cmm6QKIARZoCb4NoBFI7rOEE0WXSekE728ohEl6elKqp/KZBvwWdoB9NzBEQdfPhSTcGjvLdWnG2LCQKqHVzAk2Kr5qh4Uug/T88ly8fTprqdPxSma8lYeV/XTW+nizNQWN1FvxLONKp9tHG4eLcHsvWPNnUZE6vGqWGNqM6rprQJrzB8rtcN6pnbPzhxmrO9xruxCIuyl7FYAspIj+/pCjixPoz0g0bZ/XHC6g3/z/suDZMvSH2cfoEsGX3NGpUL/eWGxT2eag8SinG1RYF6T/OZ33MVB3B3uw+AcadqSWcDff/rHfxy++O7H4cXzt2+e3/x2+PmrVz/NZ9H+dPo/wddauwplbmRzdHJlYW0KZW5kb2JqCjExIDAgb2JqCjY5NzAKZW5kb2JqCjE2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggOTAgPj4Kc3RyZWFtCnicPYyxDcAwCAR7pmCBSIAB432iVPb+bQhx0vCnP/QeioSHSV5nwy4DT4bmUbhAg4omPJoyjaVSQ5CjJ7HpJuNS7978Z/KZFL1JDvIYKF6d94+2nXDd2nob8AplbmRzdHJlYW0KZW5kb2JqCjE3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggODggPj4Kc3RyZWFtCnicPY25EcAwCARzqqAEgXikfjyO5P5Tn/ATADvs3Fy6cmNNrFTHTD6EJGbhRRqjaJFKY+sN5Pg9FBqv/cKwo/N2Nqyuo6FbgmTaR8htV73rr1t03skLG84KZW5kc3RyZWFtCmVuZG9iagoxOCAwIG9iago8PCAvQkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMzIKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicTZJLbmsxDEPndxXaQAHrb6+nQEd5+5++I98OCiSgYkskRedJkwj596gtUUv5PJol6i16XJQ7c734/Vic92TT60vcQnTNjfeSLvFzpFxC18D3E/H+3il8UjcSh/MMKEslE4l9LprOxK0yJMPEMJBm4kjBdeDvhmwE9os54rfaJdOR8M9MbuWmrKTw8HlqYQmruVuy7EX6UNzD2TIdEfTb7LFnOly8OCEj13PR8t5MZcxwqg0bPs61gmVYw1y+2McjLxIQ3VPZaVmwpNhNVAmBMHFLTsr35qZuUxwym5Xkpq+t0pq8la2SdsiipX+DGkTG38ob9CCoZGYsB5K9oIK0hpgXHiSAfquir4mo8khfdxNU8VSfJ3WCUYmePlj8XEQR7akcm8V/yBU2r9lt2xsZDFUsORo1T6n5Voq7Yv2ete3Pip/n5z+2KnvxCmVuZHN0cmVhbQplbmRvYmoKMTkgMCBvYmoKPDwgL0JCb3ggWyAtMTAxNiAtMzUxIDE2NjAgMTA2OCBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNTMyCi9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nD2TS24mMQiE930KX2AkAwbb54k0qz/3385XdDKLFrR5uqr8lNf4YzG+n7x3rBx5ati012aMr6e9ezjx4VEjdw6vUqR8hM+RK0asPdJ2WyLzPVnUxJo0VqZq4sZwun1ej0mvZ7FG7BrHKIixNDnmHZp1e0X31fbrsX3as2Arts03fZuqkxO/bY5WodpOjLOGbdw5sakm8oIsm31hCxu7u6cJCOOHI7tb5utxLorjyxX1ijfb6a1yvwzgpm3PVQQvLblfexQot5SLXzGVQ7fKMxzkin52Tlu2KHtPYneGWf3U3KSJjwNXujEmNE7OrEF0AaPS1zpqBGXLuHlBw8weIctwA3JOPwzL9sxFwh0XBKx5hEKQXMAKXDIpLHC0AtGCZLLrNKSUb2dn2m1upgGyjEIv8sSoMkTxWxMoQ/eMvKOkJ2orVbPqjD21Xrqq4Bretyq7r1AqRXTCt0G/WHZHNe14ULaFG7i39WyZoGFY3YAgVrRHenfjT4oteF7S838cymZ75QKPTRdA3a5hYiC7EoQp9oiAAxEk53x1Z6um7Zy9G1Arly3MuJNBpwKb4YawP8+ZWgzn94HySlo9l6ca6CvPu0FCQlvfP68rUpgJvThSnzS4UIaoW7yyRB6KsgfbJHos5qd0Jrvf+7Ivk5VRWV1T1YqgskrvCxTQX67XEvHznqijkFRmS/B388/z9x+IqNR1CmVuZHN0cmVhbQplbmRvYmoKMjAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNDQgPj4Kc3RyZWFtCnicPY87EgMhDEN7TqEj4D+cZzOpNvdvoyWQBr+xsCVbKDpy8PEaqOx4STv4aZ5ONXA3Y2+TxyJTQbJrvZAZuJpORXKjDio6oeWIuRTuCS9Ou+gmm5OmD2nIJoknyt3yVySPULFhjD0udVYK7WJFk2lIp7EwIo3VE8WYDMDh4m/TXKcZfz71+h97t/cXTLgz1gplbmRzdHJlYW0KZW5kb2JqCjIxIDAgb2JqCjw8IC9CQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE4MQovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJw1UDkOBCEM63mFP7ASucN7Rtpq9v/thjBToBgcBzuDSfEhwW9ENpCJFHiCw3GNZIgxiA2qAloO0yiClzS6B79cavUSKGaJpXpISyl1XOEMltjlGjL7LqYgXZAMSA25hpZ0o3uoHE5twglGeaS25gausyaXzza6//J2SvCIduOFj9PQfJxGZdxcpHWqCHpiRs3KPTZ6CUbctRyxnLXUUqRUizpRZbDVD3M2/+7xGt8/5jc/HgplbmRzdHJlYW0KZW5kb2JqCjIyIDAgb2JqCjw8IC9CQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI1MAovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJw9UEmOAzEIvPsVfCCSCzDG72kpp8z/r1PYTqRugdlqaR5TZnT5a64pY6R8mi/d2XBGMxkzxNPkaYEubiqBFAvGrqKzOiNdwJnhKYCJL5eohjuEb0uVFyCGuePTdC55aZ8ERP5SJYvqsxhno67xy37vjV2xuHAXf2ITAo8UwVo+lBW+RdRYiTI7Mp9mM7d0Cr4mfJpxMpJuWKxKvBPZebJQa8lZxxjUx5MEG/yvA1jnOIbYok+LU7p3yr+AOL1xgjp0x+cLR9n+xVXbPZYydqZD97Yq7j3kQQCrhQhflwNoS7GC982yJg5v0G0K0R6Fc+Ge9v4HESlgAAplbmRzdHJlYW0KZW5kb2JqCjIzIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggODEgPj4Kc3RyZWFtCnicNYzBDcAwCAP/TMEClQLBoQNVfSX7f2uh8sA6Webg0KGXMxCTl/qYmK3CI11ugafGAskMmk4INIRRsKU8HEy9q6Y8sl6GN/3qLe8Hsn8XtAplbmRzdHJlYW0KZW5kb2JqCjE0IDAgb2JqCjw8IC9CYXNlRm9udCAvRGVqYVZ1U2Fucy1PYmxpcXVlIC9DaGFyUHJvY3MgMTUgMCBSCi9FbmNvZGluZyA8PCAvRGlmZmVyZW5jZXMgWyA2NSAvQSA3MiAvSCAxMDIgL2YgMTIyIC96IF0gL1R5cGUgL0VuY29kaW5nID4+Ci9GaXJzdENoYXIgMCAvRm9udEJCb3ggWyAtMTAxNiAtMzUxIDE2NjAgMTA2OCBdIC9Gb250RGVzY3JpcHRvciAxMyAwIFIKL0ZvbnRNYXRyaXggWyAwLjAwMSAwIDAgMC4wMDEgMCAwIF0gL0xhc3RDaGFyIDI1NSAvTmFtZSAvRGVqYVZ1U2Fucy1PYmxpcXVlCi9TdWJ0eXBlIC9UeXBlMyAvVHlwZSAvRm9udCAvV2lkdGhzIDEyIDAgUiA+PgplbmRvYmoKMTMgMCBvYmoKPDwgL0FzY2VudCA5MjkgL0NhcEhlaWdodCAwIC9EZXNjZW50IC0yMzYgL0ZsYWdzIDk2Ci9Gb250QkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZvbnROYW1lIC9EZWphVnVTYW5zLU9ibGlxdWUKL0l0YWxpY0FuZ2xlIDAgL01heFdpZHRoIDEzNTAgL1N0ZW1WIDAgL1R5cGUgL0ZvbnREZXNjcmlwdG9yIC9YSGVpZ2h0IDAgPj4KZW5kb2JqCjEyIDAgb2JqClsgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAKNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCAzMTggNDAxIDQ2MCA4MzggNjM2Cjk1MCA3ODAgMjc1IDM5MCAzOTAgNTAwIDgzOCAzMTggMzYxIDMxOCAzMzcgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNgo2MzYgNjM2IDMzNyAzMzcgODM4IDgzOCA4MzggNTMxIDEwMDAgNjg0IDY4NiA2OTggNzcwIDYzMiA1NzUgNzc1IDc1MiAyOTUKMjk1IDY1NiA1NTcgODYzIDc0OCA3ODcgNjAzIDc4NyA2OTUgNjM1IDYxMSA3MzIgNjg0IDk4OSA2ODUgNjExIDY4NSAzOTAgMzM3CjM5MCA4MzggNTAwIDUwMCA2MTMgNjM1IDU1MCA2MzUgNjE1IDM1MiA2MzUgNjM0IDI3OCAyNzggNTc5IDI3OCA5NzQgNjM0IDYxMgo2MzUgNjM1IDQxMSA1MjEgMzkyIDYzNCA1OTIgODE4IDU5MiA1OTIgNTI1IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMCAzMTgKMzUyIDUxOCAxMDAwIDUwMCA1MDAgNTAwIDEzNTAgNjM1IDQwMCAxMDcwIDYwMCA2ODUgNjAwIDYwMCAzMTggMzE4IDUxOCA1MTgKNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUyMSA0MDAgMTAyOCA2MDAgNTI1IDYxMSAzMTggNDAxIDYzNiA2MzYgNjM2IDYzNiAzMzcKNTAwIDUwMCAxMDAwIDQ3MSA2MTcgODM4IDM2MSAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDYzNiA2MzYgMzE4IDUwMAo0MDEgNDcxIDYxNyA5NjkgOTY5IDk2OSA1MzEgNjg0IDY4NCA2ODQgNjg0IDY4NCA2ODQgOTc0IDY5OCA2MzIgNjMyIDYzMiA2MzIKMjk1IDI5NSAyOTUgMjk1IDc3NSA3NDggNzg3IDc4NyA3ODcgNzg3IDc4NyA4MzggNzg3IDczMiA3MzIgNzMyIDczMiA2MTEgNjA4CjYzMCA2MTMgNjEzIDYxMyA2MTMgNjEzIDYxMyA5OTUgNTUwIDYxNSA2MTUgNjE1IDYxNSAyNzggMjc4IDI3OCAyNzggNjEyIDYzNAo2MTIgNjEyIDYxMiA2MTIgNjEyIDgzOCA2MTIgNjM0IDYzNCA2MzQgNjM0IDU5MiA2MzUgNTkyIF0KZW5kb2JqCjE1IDAgb2JqCjw8IC9BIDE2IDAgUiAvSCAxNyAwIFIgL2YgMjAgMCBSIC96IDIzIDAgUiA+PgplbmRvYmoKMjggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNTkgPj4Kc3RyZWFtCnicPVJJcsMwDLv7FXwCd0nvSacn5//XAvTUlxBjigAIpneLytn4aStZfuTHLjtLIrd8B22T+4qqB6RugswlxyVXiFnK50qQWLSUmVifqQ7KzzWoVfjCT8xMTIckEUvIST2KsH5eB/egfr2k81tk/KNjg9JbkkwFnRrulaOU2LBUnxrkHjTdlFafmXZlByyNN2SlJnX69dPjB0swpS8S0UGIxJ/kcocsCykH8Xau3kB4V7sg1VMrDztEmo+R3lIFqzkzAUtG0w4jYG3WmCBVArxFawi0FuLyhU4rIj45N3QwTVWehciwUuFYe89oDRe6hrzScHqScf/5H7wr3tfvH9rzZmQKZW5kc3RyZWFtCmVuZG9iagoyOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIzMiA+PgpzdHJlYW0KeJw1UTtyBTEI630KXSAz5m+fZzOvSu7fRrCTZmEBCQnnPdiIxJcY0h3lim9ZnWYZfieLvPhZKZy8F1GBVEVYIe3gWc5qhsFzI1PgciY+y8wn02LHAqqJOM6OnGYwCDGN62g5HWaaBz0h1wcjbuw0y1UMab1bqtf3Wv5TRfnIupvl1imbWqlb9Iw9icvO66kt7QujjuKmINLhY4f3IF/EnMVFJ9LNfjPlsJI0BKcF8CMxlOrZ4TXCxM+MBE/Z0+l9lIbXPmi6vncv6MjNhEzlFspIxZOVxpgxVL8RzST1/T/Qsz5/mjBURwplbmRzdHJlYW0KZW5kb2JqCjMwIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNzcgPj4Kc3RyZWFtCnicMzc1UjBQsLQAEmamJgrmRpYKKYZcQD6IlctlaGkOZuWAWSbGBkCWqakpEgsiC9MLYcHkYLSxiTnUBAQLJAe2NgdmWw5XGgCe4BuaCmVuZHN0cmVhbQplbmRvYmoKMzEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMTIgPj4Kc3RyZWFtCnicNVA5DgMxCOz9ivlAJINtMO/ZKF3+34YBpVgxWubCfh0Tx/CSBV8C34q3jBUbZorvWKqF1A5sHagunKt4hlzB0QuxiZ0WnMs2N4nUFWRIRGlkW27oEoo2Rafk701zSzfl9qRJ021aGZh6GXJ2BBFDyWAJaroWTVi0PRX/U546ivd9xw4rdNzh05Mf9T3DZz6HS73F9qjZiUS6L8iQ05pLCU002dGvyBTOPDakkM4gQVJcgmtlkO3pl6MDEjAxtyxAdleinCVpx9L/M57x+QEB21OpCmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0JCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjM3Ci9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nD1Ru3HFMAzrPQVG4Ef8aJ53lyrZvw0oOSl4gCkRBOSnLNGFn2eI4PtZ7v/IA5KtUG2EJzQVkQ3TwOdJEVhupCbcXtznhGyVI/biXCDCEO08CWmkCxY7GQveFz+Pqx5mrLlh/L4zmn1UdNVRHbx7DuNmTT9OlN3rzayOW5v7dO+uE4drSCaf9x+clEqnlyyDOku4sDaaGtbjvCjGWMw4/ieqsE2ytqMKwdIlSCrQgBhKEsaAxS3+IidaDgvamxtp653JTqo0ioYXowzeoPVGOIp0kXyYayuDsamYNr755CU36Ptnv5+vXwNrWusKZW5kc3RyZWFtCmVuZG9iagozMyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIyNyA+PgpzdHJlYW0KeJxFkEuOAyEQQ/ecwkeg/nCejrLq3H87LjrRbLAlKNczuQMTe/HITJRuvGS4O8wVn+EZMHP4SphsxEzoTlwjlK4U4VSfCI7L3rzpoIl7RM6jngVZ1c4NagFnkuaC7YIu54wVN87JrUblzfSj1xC+aXcf13mH9kjj3sNUvs451c67ighpC1nVtL6QbBTJDms/Kk3bzssQseBsGlboHN4Iu1d3J0sYfr/yMCUTPw/d+lF8XTej6xRnJ1cma8956EnpX/XKow/FcSnoF7HtzCT3X6dTkqlTe2fvaf2nuMf7D5BuVjkKZW5kc3RyZWFtCmVuZG9iagozNCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMwNCA+PgpzdHJlYW0KeJw9kjuSwzAMQ3udghfIjPiT5PNkJ5X3/u0+MslWgEmJACgvdZmypjwgaSYJ/9Hh4WI75XfYns3MwLVELxPLKc+hK8TcRfmymY26sjrFqsMwnVv0qJyLhk2TmucqSxm3C57DtYnnln3EDzc0qAd1jUvCDd3VaFkKzXB1/zu9R9l3NTwXm1Tq1BePF1EV5vkhT6KH6UrifDwoIVx7MEYWEuRT0UCOs1yt8l5C9g63GrLCQWpJ57MnPNh1ek8ubhfNEA9kuVT4TlHs7dAzvuxKCT0StuFY7n07mrHpGps47H7vRtbKjK5oIX7IVyfrJWDcUyZFEmROtlhui9We7qEopnOGcxkg6tmKhlLmYlerfww7bywv2SzIlMwLMkanTZ44eMh+jZr0eZXneP0BbPNzOwplbmRzdHJlYW0KZW5kb2JqCjM1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNTQgPj4Kc3RyZWFtCnicMzY2VzBQMDQyV9A1MjZVMDI0UDA3M1FIMeSCMXPBLLBsDhdcIYQJks+Bq8zhSgMATJAPFQplbmRzdHJlYW0KZW5kb2JqCjM2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjc5ID4+CnN0cmVhbQp4nD1SO5LFIAzrcwpfgBnwF86Tna2y929XgrxXZKxERpId0lK6DA1pI1ViDKns8jMuwrZU/g4i+1w+v9DWOtCch6OLjQmgKfelqwN2Fa2SFr7rKDIE5hDYaJpoTlFwCgm1fdpwkIf6AOsyIna9LwYlejayrUP2IPYTqRlSQTnwjoRQhIfNvmP4OHE87c0TYE6eDDgje/UzTildOWE5FDAyt8MtsN7XZ1/PRrmIvOYHYQ4ixyJyYlMTDJJAsRxejnTw1FOjNgPkUVwwUcdsscDPvWc+6DGkU+iR7dhcLqReZPCF+dmh8GA/twAGKqq1nQY7WL2/jmO9hg2/j+Fa5I7bii0coE0XDsQ7wRFZ7+8tea7ffwdybgYKZW5kc3RyZWFtCmVuZG9iagozNyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI3NiA+PgpzdHJlYW0KeJw9UkuO6DAI2+cUXCBS+CY9T0ez6rv/9tm0mhUWYGNIykuWqKVMLZNUlV1LfnR07jL5NzSvRs+w9ebMQ+ZJsTgyt8o9DOSZW6zQa2/UqwsAsUju1BLbJcaWS8WSZIes7RB3ZNDhxSrZzPjawg43a45HUhcqXqcHBfmMMPBOzH2+iWUhNFcZbbfAQQ8WqAM9MAsTuSLj3WsTPY14C6CsD5m/iC431FyPbEyAU7jaC96plNYxDxWJohzsRhq9n6PmOKHD2z1iOfZyCUcG3uJox3vwRYieRlZErH7IsxH5hg2pSI+Yyhvqbh96/I2t2Gh/diZJwddf1ttMNdK54NRcrdZfg0do8N6o4fP3S57x+x8hJm4SCmVuZHN0cmVhbQplbmRvYmoKMzggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMzAgPj4Kc3RyZWFtCnicNVFJbsMwDLzrFfOBAOIuv8dBT+3/rx3SCWBgaEuczREbGxF4icHPQeTGW9aMmvibyV3xuzwVHgm3gidRBF6Ge9kJLm8Yl/04zHzwXlo5kxpPMiAX2fTwRMhgl0DowOwa1GGbaSf6hoTPjkg1G1lOX0vQS6sQKE/ZfqcLSrSt6s/tsy607WtPONntqSeVTyCeW7ICl41XTBZjGfRE5S7F9EGqs4WehPKifA6y+aghEl2inIEnBgejQDuw57afiVeFoHV1n7aNoRopHU//NjQ1SSLkEyWc2dK4W/j+nnv9/AOmVFOfCmVuZHN0cmVhbQplbmRvYmoKMzkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA2OCA+PgpzdHJlYW0KeJwzNjZXMFAwNASRRkYGCqZAVoohF0jA0MhEIZcLJAhi5YBZBkAaojgHrgbCAmmEqAaxIKqNLY2hsggWRDYNAEeiFssKZW5kc3RyZWFtCmVuZG9iago0MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDY2ID4+CnN0cmVhbQp4nDM2tFAwUDA3V9A1NDRVMDIyUDA0MlFIMeQyNDQHM3O5YII5YJaJAZBhCCTBGnK4YFpzwDogslCtOVxpAE04EfUKZW5kc3RyZWFtCmVuZG9iago0MSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIyNyA+PgpzdHJlYW0KeJw1TzuyAyEM6zmFLpAZjG1gz7OZVC/3b59ksg0S/kjy9ERHJl7myAis2fG2FhmIGfgWU/GvPe3DhOo9uIcI5eJCmGEknDXruJun48W/XeUz1sG7Db5ilhcEtjCT9ZXFmct2wVgaJ3FOshtj10RsY13r6RTWEUwoAyGd7TAlyBwVKX2yo4w5Ok7kiediqsUuv+9hfcGmMaLCHFcFT9BkUJY97yagHRf039WN30k0i14CMpFgYZ0k5s5ZTvjVa0fHUYsiMSekGeQyEdKcrmIKoQnFOjsKKhUFl+pzyt0+/2hdW00KZW5kc3RyZWFtCmVuZG9iago0MiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0NSA+PgpzdHJlYW0KeJxFULuNQzEM6z0FFwhg/Sx7nndIldu/PUpGcIUhWj+SWhKYiMBLDLGUb+JHRkE9C78XheIzxM8XhUHOhKRAnPUZEJl4htpGbuh2cM68wzOMOQIXxVpwptOZ9lzY5JwHJxDObZTxjEK6SVQVcVSfcUzxqrLPjdeBpbVss9OR7CGNhEtJJSaXflMq/7QpWyro2kUTsEjkgZNNNOEsP0OSYsyglFH3MLWO9HGykUd10MnZnDktmdnup+1MfA9YJplR5Smd5zI+J6nzXE597rMd0eSipVX7nP3ekZbyIrXbodXpVyVRmY3Vp5C4PP+Mn/H+A46gWT4KZW5kc3RyZWFtCmVuZG9iago0MyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDM5MiA+PgpzdHJlYW0KeJw9UktuBTEI288puECl8E1ynqne7t1/W5vMVKoKLwO2MZSXDKklP+qSiDNMfvVyXeJR8r1samfmIe4uNqb4WHJfuobYctGaYrFPHMkvyLRUWKFW3aND8YUoEw8ALeCBBeG+HP/xF6jB17CFcsN7ZAJgStRuQMZD0RlIWUERYfuRFeikUK9s4e8oIFfUrIWhdGKIDZYAKb6rDYmYqNmgh4SVkqod0vGMpPBbwV2JYVBbW9sEeGbQENnekY0RM+3RGXFZEWs/PemjUTK1URkPTWd88d0yUvPRFeik0sjdykNnz0InYCTmSZjncCPhnttBCzH0ca+WT2z3mClWkfAFO8oBA7393pKNz3vgLIxc2+xMJ/DRaaccE62+HmL9gz9sS5tcxyuHRRSovCgIftdBE3F8WMX3ZKNEd7QB1iMT1WglEAwSws7tMPJ4xnnZ3hW05vREaKNEHtSOET0ossXlnBWwp/yszbEcng8me2+0j5TMzKiEFdR2eqi2z2Md1Hee+/r8AS4AoRkKZW5kc3RyZWFtCmVuZG9iago0NCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDcxID4+CnN0cmVhbQp4nLMwtlAwUDA0MFMwNDdSMDc2UjAxNVFIMeQCCYGYuVwwwRwwyxioLAcsi2BBZEEsI1NTqA4QC6LDEK4OwYLIpgEA6+cYMgplbmRzdHJlYW0KZW5kb2JqCjQ1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTMzID4+CnN0cmVhbQp4nE2PQRLDMAgD736FnoCxAfOedHpK/n8tkDbuBe2MgJGGMAg8YgzrMCW8evvhVaRLcDaO+SUZRTwIagvcF1QFR2OKnfjY3aHspeLpFE2L6xFz07SkdDdRKm29ncj4wH2f3h9VtiSdgh5b6oQu0STyRQJz2FQwz+rGS0uPp+3Z3h9mPjPXCmVuZHN0cmVhbQplbmRvYmoKNDYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNDcgPj4Kc3RyZWFtCnicTVG7bUQxDOvfFFzgAOtreZ4LUl32b0PJCJDCIKEvKaclFvbGSwzhB1sPvuSRVUN/Hj8x7DMsPcnk1D/muclUFL4VqpuYUBdi4f1oBLwWdC8iK8oH349lDHPO9+CjEJdgJjRgrG9JJhfVvDNkwomhjsNBm1QYd00ULK4VzTPI7VY3sjqzIGx4JRPixgBEBNkXkM1go4yxlZDFch6oCpIFWmDX6RtRi4IrlNYJdKLWxLrM4Kvn9nY3Qy/y4Ki6eH0M60uwwuileyx8rkIfzPRMO3dJI73wphMRZg8FUpmdkZU6PWJ9t0D/n2Ur+PvJz/P9CxUoXCoKZW5kc3RyZWFtCmVuZG9iago0NyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDkwID4+CnN0cmVhbQp4nE2NQRLAIAgD77wiT1BE0P90etL/X6vUDr3ATgKJFkWC9DVqSzDuuDIVa1ApmJSXwFUwXAva7qLK/jJJTJ2G03u3A4Oy8XGD0kn79nF6AKv9egbdD9IcIlgKZW5kc3RyZWFtCmVuZG9iago0OCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzOCA+PgpzdHJlYW0KeJxFUktyxTAI2+cUXCAz5mfj87xOV+n9t5VwOt089AwICTI9ZUim3DaWZITkHPKlV2SI1ZCfRo5ExBDfKaHArvK5vJbEXMhuiUrxoR0/l6U3Ms2u0Kq3R6c2i0Y1KyPnIEOEelbozO5R22TD63Yh6TpTFodwLP9DBbKUdcoplARtQd/YI+hvFjwR3Aaz5nKzuUxu9b/uWwue1zpbsW0HQAmWc95gBgDEwwnaAMTc2t4WKSgfVbqKScKt8lwnO1C20Kp0vDeAGQcYOWDDkq0O12hvAMM+D/SiRsX2FaCoLCD+ztlmwd4xyUiwJ+YGTj1xOsWRcEk4xgJAiq3iFLrxHdjiLxeuiJrwCXU6ZU28wp7a4sdCkwjvUnEC8CIbbl0dRbVsT+cJtD8qkjNipB7E0QmR1JLOERSXBvXQGvu4iRmvjcTmnr7dP8I5n+v7Fxa4g+AKZW5kc3RyZWFtCmVuZG9iago0OSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE2MyA+PgpzdHJlYW0KeJxFkLl1BDEMQ3NVgRJ4gDrqGT9Hs/2nC2m83kD6eIR4iD0Jw3JdxYXRDT/etsw0vI4y3I31Zcb4qLFATtAHGCITV6NJ9e2KM1Tp4dVirqOiXC86IhLMkuOrQCN8OrLHQ1vbmX46r3/sIe8T/yoq525hAS6q7kD5Uh/x1I/ZUeqaoY8qK2seatq/CLsilLZ9XE5lnLp7B7TCZytX+30DqOc6gAplbmRzdHJlYW0KZW5kb2JqCjUwIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNTIgPj4Kc3RyZWFtCnicMzYzVDBQMLFUMDI2UTA2NAJiE4UUQy6gCIiVywUTywGzQKpyuKDKc2CqcrjSAOkJDcAKZW5kc3RyZWFtCmVuZG9iago1MSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDY4ID4+CnN0cmVhbQp4nDMyt1AwULA0ARKGFiYK5mYGCimGXEC+qYm5Qi4XSAzEygGzDIC0JZyCiFtCNEGUglgQpWYmZhBJOAMilwYAybQV5QplbmRzdHJlYW0KZW5kb2JqCjUyIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggODEgPj4Kc3RyZWFtCnicPcy7FYAwCAXQPlO8EUJ8gOzjsdL9W8FEG7h81QMdIRnUDW4dh7SsS3eTfep6tYmkyIDSU2pcGk6MqGl9qX1q4Lsb5kvViT/Nz+cDh8cZawplbmRzdHJlYW0KZW5kb2JqCjUzIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNDUgPj4Kc3RyZWFtCnicMzK3UDBQsDQBEoYWJgrmZgYKKYZclhBWLhdMLAfMAtGWcAoingYAn30MtQplbmRzdHJlYW0KZW5kb2JqCjU0IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjU1ID4+CnN0cmVhbQp4nEWRS5IDIAhE956CI4D85DyZmlVy/+00mEw2dpeo/YRKI6YSLOcUeTD9yPLNZLbptRyrnY0CiiIUzOQq9FiB1Z0p4sy1RLX1sTJy3Okdg+IN566cVLK4UcY6qjoVOKbnyvqq7vy4LMq+I4cyBWzWOQ42cOW2YYwTo81Wd4f7RJCnk6mj4naQbPiDk8a+ytUVuE42++olGAeCfqEJTPJNoHWGQOPmKXpyCfbxcbvzQLC3vAmkbAjkyBCMDkG7Tq5/cev83v86w53n2gxXjnfxO0xru+MvMcmKuYBF7hTU8z0XresMHe/JmWNy031D51ywy91Bps/8H+v3D1CKZogKZW5kc3RyZWFtCmVuZG9iago1NSAwIG9iago8PCAvQkJveCBbIC0xMDIxIC00NjMgMTc5NCAxMjMzIF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzNwovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJzjMjQwUzA2NVXI5TI3NgKzcsAsI3MjIAski2BBZNMAAV8KCgplbmRzdHJlYW0KZW5kb2JqCjU2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTYxID4+CnN0cmVhbQp4nEWQSxLDIAxD95xCR/BHBnyedLpK77+tIU2zgKexQAZ3JwSptQUT0QUvbUu6Cz5bCc7GeOg2bjUS5AR1gFak42iUUn25xWmVdPFoNnMrC60THWYOepSjGaAQOhXe7aLkcqbuzvlHcPVf9Uex7pzNxMBk5Q6EZvUp7nybHVFd3WR/0mNu1mt/FfaqsLSspeWE285dM6AE7qkc7f0FqXM6hAplbmRzdHJlYW0KZW5kb2JqCjU3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzIwID4+CnN0cmVhbQp4nDVRu3HFMAzrNQUX8J34lTSPc6/K278NQDsVYRoEQKq8ZEq5XOqSVbLC5EeH6hRN+T5gpvwO9ZDj6B7ZIbpT1pZ7GAjLxDyljlhNlnu4BYEvDE2JuYXz9wjoKwajMBOBusXfP0CzJDBpcPBTkGutWmKJDjwsFlizK8ytGilUyFV8Oza5BwVycbPQpxyaFLfcgvBliGRHarGvy2Up8rv1CRiEFeaITxSJheeBDmYi8ScDYnv22WJXVy+qERnWSYcHUgTSbG4SMDRFsuqDG9hXxzU/T0fZwclBv4rB+DY4mS9JeV8FoRCPF/4Oz9nIsZJDJBTyfbXAiCNsgBGhT+0jEGUgNEX37plSPiZViu8ARiEcfapXMrwXkdlqhs3/GV3ZKgoGVVkfn0ZwJoNJOPNkowrTUrXTv/vc4/MHY2N6gAplbmRzdHJlYW0KZW5kb2JqCjU4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjE0ID4+CnN0cmVhbQp4nD1QuxFDMQjrPQUL5M587TfPy6XL/m0knKRCNkISlJpMyZSHOsqSrClPHT5LYoe8h+VuZDYlKkUvk7Al99AK8X2J5hT33dWWs0M0l2g5fgszKqobHdNLNppwKhO6oNzDM/oNbXQDVocesVsg0KRg17YgcscPGAzBmROLIgxKTQb/rXL3UtzvPRxvooiUdPCu+eX0y88tvE49jkS6vfmKa3GmOgpEcEZq8op0YcWyyEOk1QQ1PQNrtQCu3nr5N2hHdBmA7BOJ4zSlHEP/1rjH6wOHilL0CmVuZHN0cmVhbQplbmRvYmoKNTkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MCA+PgpzdHJlYW0KeJxFjLsNwDAIRHumYAR+JmafKJWzfxsgStxwT7p7uDoSMlPeYYaHBJ4MLIZT8QaZo2A1uEZSjZ3so7BuX3WB5npTq/X3BypPdnZxPc3LGfQKZW5kc3RyZWFtCmVuZG9iago2MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIzNiA+PgpzdHJlYW0KeJxNUEtuRCEM23OKXOBJJCEBzkPVVef+27HDVO0qhhh/SA/pslUe61NidYns8qVNl8oyeRWo5U/b/1EMAm7/0MhBtLeMnWLmEtbFwiQ85TQjGyfXLB+PO08bZoXGxI3jnS4ZYJ8WATVblc2BOW06N0C6kBq3qrPeZFAMIupCzQeTLpyn0ZeIOZ6oYEp3JrWQG1w+1aEDcVq9Crlji5NvxBxZocBh0Exx1l8B1qjJslnIIEmGIc59o3uUCo2oynkrFcIPk6ER9YbVoAaVuYWiqeWS/B3aAjAFtox16QxKgaoAwd8qp32/ASSNXVMKZW5kc3RyZWFtCmVuZG9iago2MSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE0NyA+PgpzdHJlYW0KeJw9T7kNAzEM6z0FFzjAeixb81yQ6rJ/G8pGUggiQPGRZUfHClxiApOOORIvaT/4aRqBWAY1R/SEimFY4G6SAg+DLEpXni1eDJHaQl1I+NYQ3q1MZKI8rxE7cCcXowc+VBtZHnpAO0QVWa5Jw1jVVl1qnbACHLLOwnU9zKoE5dEnaykfUFRCvXT/n3va+wsAby/rCmVuZHN0cmVhbQplbmRvYmoKNjIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNDkgPj4Kc3RyZWFtCnicNY9LDgMhDEP3OYUvMFJ+hHAeqq6m9982YVoJCQvbL8EWg5GMS0xg7Jhj4SVUT60+JCOPukk5EKlQNwRPaEwMM2zSJfDKdN8ynlu8nFbqgk5I5OmsNhqijGZew9FTzgqb/svcJGplRpkDMutUtxOysmAF5gW1PPcz7qhc6ISHncqw6E4xotxmRhp+/9v0/gJ7MjBjCmVuZHN0cmVhbQplbmRvYmoKNjMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA0OSA+PgpzdHJlYW0KeJwzNrRQMFAwNDAHkkaGQJaRiUKKIRdIAMTM5YIJ5oBZBkAaojgHriaHKw0AxugNJgplbmRzdHJlYW0KZW5kb2JqCjY0IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTU3ID4+CnN0cmVhbQp4nEWQuRFDMQhEc1VBCRKwCOqxx9F3/6kX+Uq0bwAth68lU6ofJyKm3Ndo9DB5Dp9NJVYs2Ca2kxpyGxZBSjGYeE4xq6O3oZmH1Ou4qKq4dWaV02nLysV/82hXM5M9wjXqJ/BN6PifPLSp6FugrwuUfUC1OJ1JUDF9r2KBo5x2fyKcGOA+GUeZKSNxYm4K7PcZAGa+V7jG4wXdATd5CmVuZHN0cmVhbQplbmRvYmoKNjUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMzIgPj4Kc3RyZWFtCnicLVI5jiQxDMv9Cn5gAOvy8Z4eTNT7/3RJVQUFqmzLPORyw0QlfiyQ21Fr4tdGZqDC8K+rzIXvSNvIOohryEVcyZbCZ0Qs5DHEPMSC79v4GR75rMzJswfGL9n3GVbsqQnLQsaLM7TDKo7DKsixYOsiqnt4U6TDqSTY44v/PsVzF4IWviNowC/556sjeL6kRdo9Ztu0Ww+WaUeVFJaD7WnOy+RL6yxXx+P5INneFTtCaleAojB3xnkujjJtZURrYWeDpMbF9ubYj6UEXejGZaQ4AvmZKsIDSprMbKIg/sjpIacyEKau6Uont1EVd+rJXLO5vJ1JMlv3RYrNFM7rwpn1d5gyq807eZYTpU5F+Bl7tgQNnePq2WuZhUa3OcErJXw2dnpy8r2aWQ/JqUhIFdO6Ck6jyBRL2Jb4moqa0tTL8N+X9xl//wEz4nwBCmVuZHN0cmVhbQplbmRvYmoKNjYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA2OCA+PgpzdHJlYW0KeJwzMzZTMFCwMAISpqaGCuZGlgophlxAPoiVywUTywGzzCzMgSwjC5CWHC5DC2MwbWJspGBmYgZkWSAxILrSAHL4EpEKZW5kc3RyZWFtCmVuZG9iago2NyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMxNyA+PgpzdHJlYW0KeJw1UktyQzEI279TcIHOmL99nnSyau6/rYQnK7AtQEIuL1nSS37UJdulw+RXH/clsUI+j+2azFLF9xazFM8tr0fPEbctCgRREz34MicVItTP1Og6eGGXPgOvEE4pFngHkwAGr+FfeJROg8A7GzLeEZORGhAkwZpLi01IlD1J/Cvl9aSVNHR+Jitz+XtyqRRqo8kIFSBYudgHpCspHiQTPYlIsnK9N1aI3pBXksdnJSYZEN0msU20wOPclbSEmZhCBeZYgNV0s7r6HExY47CE8SphFtWDTZ41qYRmtI5jZMN498JMiYWGwxJQm32VCaqXj9PcCSOmR0127cKyWzbvIUSj+TMslMHHKCQBh05jJArSsIARgTm9sIq95gs5FsCIZZ2aLAxtaCW7eo6FwNCcs6Vhxtee1/P+B0Vbe6MKZW5kc3RyZWFtCmVuZG9iago2OCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDUyID4+CnN0cmVhbQp4nDM2NlcwAEJdSyMFYyDb3MhSIcWQy8jUBMzM5YIJ5nBZGINV5XAZQGmYohyuNADfqg2tCmVuZHN0cmVhbQplbmRvYmoKNjkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNyA+PgpzdHJlYW0KeJwzNrRQMIDDFEMuABqUAuwKZW5kc3RyZWFtCmVuZG9iago3MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMSA+PgpzdHJlYW0KeJxFj8sNBCEMQ+9U4RLyGT6ph9We2P6v6zCaQUL4QSI78TAIrPPyNtDF8NGiwzf+NtWrY5UsH7p6UlYP6ZCHvPIVUGkwUcSFWUwdQ2HOmMrIljK3G+G2TYOsbJVUrYN2PAYPtqdlqwh+qW1h6izxDMJVXrjHDT+QS613vVW+f0JTMJcKZW5kc3RyZWFtCmVuZG9iago3MSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzOCA+PgpzdHJlYW0KeJw1Ujmu3UAM630KXSCAds2c5wWpfu7fhpRfCkO0VoqajhaVafllIVUtky6/7UltiRvy98kKiROSVyXapQyRUPk8hVS/Z8u8vtacESBLlQqTk5LHJQv+DJfeLhznY2s/jyN3PXpgVYyEEgHLFBOja1k6u8Oajfw8pgE/4hFyrli3HGMVSA26cdoV70PzecgaIGaYlooKXVaJFn5B8aBHrX3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       "     <use x=\"950.537109\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "     <use x=\"978.320312\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "     <use x=\"1017.529297\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p6fc094d883\">\n",
       "   <rect height=\"157.5\" width=\"253.636364\" x=\"50.595312\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pd355d9a684\">\n",
       "   <rect height=\"157.5\" width=\"253.636364\" x=\"50.595312\" y=\"211.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p595520d7a9\">\n",
       "   <rect height=\"253.636364\" width=\"253.636364\" x=\"354.958949\" y=\"68.749943\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fc = 1000  # Hz\n",
    "B, A, b, a = audiofilter.biquad_lp2nd(fc, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"highpass1st\"></a>\n",
    "### 1st Order Highpass `hp1st`\n",
    "\n",
    "\\cite{TietzeSchenk2008}, \\cite{Moschytz1981}\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| 0  | $\\frac{1}{\\omega_\\text{c}}$ | 0 | 0 | $\\frac{1}{\\omega_\\text{c}}$ | 1 |\n",
    "\n",
    "with cut frequency $\\omega_c=2 \\pi f_c$ in rad/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [0.                     0.00015915494309189535 0.                    ]\n",
      "A = [0.0000000000000000e+00 1.5915494309189535e-04 1.0000000000000000e+00]\n",
      "b = [ 0.9384882314963784  0.                 -0.9384882314963784]\n",
      "a = [ 1.                   0.12302353700724311 -0.8769764629927569 ]\n"
     ]
    },
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4RotVOAT56GyBfkokrsp1QCt5KWvNUtnrSVKjpSuawcNCJoPgwdnEMmDsDCLWtFJQjKAi4e2S0+ulZaCUppYyZkkLzdbmwRNmMqXiFwuiFDlKooCHxmNcfQcBhykLbCVZzOUuQh7qOwIYyW9LHs9L0o91yZX3ArWIYSa8FwKafpDBdclhbKD5zmHZ698JUQ1TTsKDO2+cpTLGiBcxpAIEDipM3BfNUkqSdZAC+LD0xmRTiqTxgCAtJbbEogyy+S+VwFRaHngpIopd4kR9ATIiTWZj5ZAGcGAIvq/7BwaM8Dcw6A4zycSlotjJlASOwEAuVInZlvp1CwzgYP3QjSH5bHs+XsyJyMRSWh4TSXGxlAjLjBsnR5uUMR5vSmm5nO0AScmYErqRKujyPOQlGDqDPwnLnMp4pKzZWiunaQS0DcCIbY1wKbZyPpW2BZfok/L7NXbwWarve+WXFgLnyg8UZ3Sfo4tzuu/65hZT1YebtzOqj8DL5DnVj8x5RvVhcENpf6v6zKG0e5iqfmSIf679WHb6ZhUT7QevvhXARPstc197P9X+5PsuDQRIbPBRtBBaJUX5adD+mDnnULQ/ILanOGh/hlEYX0rrkqUYCp1hCskE+TxmXfFHpu8mAWjxL8lQt9iYWdPXtQNCmAcLyniTh+PJpbLdZ8xEAiKi+xC7V04bMHoP00pFx53tYxLpUoBHDHyHqLiL0fStM7AFxCA52F5nrbQRmOpyAE7s0pmOK/rd6+OXK3/umuN2l+PAuwUrO9fGQ6uyH0+DsSTN18b/+O2zD3eoiw9Bb0Jm6uIruamLr2RV0y7E87p4sdSZunixsJm6eEnlPq+Lp7EVgB7aSHyu5RipN4fgh3L1SoR7OH+TJqbK052LcNNQR3Hri0Zc5pC9v7r4UFFJVEuxZqi3qQLOQRcBI4g8KwKei1KfnYJI+JmmgPdSKfir+WD05lLJ6oUodSgcPq8Pvu9y/Ms/+bUg/4spyMeCCh87jP/6puXTq/GVGQY/Z4bBrzfDYP//mOEdmgCssMJf2wD82gZgrzYAt/FHd+0BwD5ICy+o/zFh8qPEiVI3YHIf4FbiTSXCDXRBei2VVliVQ0MfOwHUB+RP5Sjh6HQTO/nnuJt1Bzno0950cH2a9NXkCexek0AmPaFKsyFs6bMrGwa8xTn4R0WG18DAsDtCVG8gB5QO4aOXoA27W0nmt5JIAekkGsP+rhOtl92ibEYzxchH7ImxA5Z+iQibEJRTCoi4FRW/MrQZBgtFxgaSQxJAFGMpFQrZR9sMQ7ZcjMAwFB510AyhMDZnMIwqH8vBSUKUHI4KDEV9fnBePijJPlY/bGVTHRkbPsXYGfGuse/xpoYhzaOyxc7b60FLTyTpySht6KqAmqrQUGQFnWKsYFbDaCZFDVpNYZWvTvasYgwx9ufSWXtozr+bw2lAVAKBmNx5bVZFQpukIjd2dqfqrEXWgN6d7B1YwMZ0WMHyaYilB2NOQDxgG1QgKbCU2EIdcJ95Yew7R9d2ODsVnrqyN69/+PhBHwTvOSfQns5Z6YKqcavU1TOyxPj6fDiYptTPBm+SDXedD+ycf7HzUe23wU25uNUzssh6Zk7ali0Re3oKpRchHm9npQe++Zq5J5Bw610kmHS7/ivyaiCXWS8B6RlhZ5BmqoiEZ3H0XwyOdTFvhK3k9Tgusl7EMUu46LHIcTJ2Bkjq1CfH6l3woA+9Fktk4s+8C3wKZjK4Yb8wu6n824W4WO3t/noK57E91lsGxeV/V39P/Pqb98++/+nj+y/Fdal4WcekY3BdiXdc2+f5yh0LcUqeXdtJGiqbAZVjpi6aGCglQ/FWa/svdnFXyMkXFUTB8uFNTYmirp6ThrOalJb30qzItxpvM5xI+ap0iyU+/mLXeA0eWJPLZG0zLZW6flo0Zz0tDe/FaXFwqd5KxCYt6G8Tef1dWEsi2X1iO9BMS6WunxbNWU9Lw3txWmL/YR5Dg+O7zbTYvwdrqdtqNSuVuHpSNF81Jw3nmehDThVy8qdJkW7z6ooj05kvJhjWsnKGJgXJi9EgVup6FDVnDWPD+xY4Su0jZYIGuxwa/f3SsAypc5xgbA2WlboeS81ZY9nwvgWWwXWSgGTY5GwbF/2lYZmj3EIQcrMSKup6LDVnjWXD+xZYZpaUrERw0yk1UcgXhqU67lRYKupqLBvOCsuW9zKWLJVEKRBj35i4CbQn6aFMtsN2efjk199J3WSK5miHD1Zf5C7tX7bYpdEpCXlQk+bbwSTxbfbQvt91W8pRTsApdM6bWHIevbSuMexsf/Wzyc6UG12ELhmGTvqZRkn6kKQUoQfEl8xWrqORQ7xh++6zNMXj/ibjZEIsSaUeNsVyhA25nRNzlCadQiesGdnKZwGEoIHZs+SCebksNdkoXVS93F3Khgv3BFtO2cvHhSDX1GBGcqG7ThIY5fxeElIweNvTEW5Ba7DVKNfaBGd7qRBYZblQhfprbQBD/3z0cvuTx46xzxijkuLmo9RPZJJpk1mE1IUsXjqzQYwtKZTl+hxb6HMfO4QuUyY7n3IhjZXQrqAjemLkAqSS+ANpe3A8trAumnIBTMEPf4QuOY3WeLk0A7GIXLITilAO75KPonLXS5YblYIrdI6do2Dleam9CTn2U8h4Hhtk+dJBHlrujCnPY56xbYbLLHdosol9eqq3AFNaHWbQsV9AENuLBT0C9LCpcvUnUCoXFkHx5R4huIDiBgIALUdHXtLMwuBOuEshxiKuE9Ghr0FcmJOsVSopepBakryDiFVa9Ec8JHTJU7QQyxV6dsOdY/OfiUCPAoMY/uT5CJhDyvIJquEfyhfgcotVMx7pdhqLo9Wjl0wnH5hcK60TtTY2kGvAcWIFNkvKbYMlFn0orMxDA72TylcMUjpe6qlyVjCwkkfaTK18SIq55Lo2quAk7ZdKll2jOo6AcSafJqrm5AolluSrRjMdpjA4GFFoFXn+89rNgbPkhXoBoTEUhlvAi/zEruT2G7hwycPVVshi/JIj6FujlYt8oMXFdWkjZ7mkCjyjbZ2C3AqTsAYUZ6GcCEfosVSPuNbpMF7mKcv3w8ZJcSz57pKu3Tg1hkLJxVocWyfI5cJr/C63LlPoBlonl2NpFysXXeJdfZdF5ZLla5eEzTxx4bMfJtvHMW+SKBJdy54wt3BkwK0dDmW51S2y4Xb4kirI5vT9vIorjXgwguhCCw9Jgzu5xM63cEq5DjjmMIGfYHoBvxtsO13SvMkbsqUCQE0vwYHi6RipVQdJv/bigWKrPuTKrXquf75qm9yxRnL5WqubJCff3g/kUZXh37EBN7ZkWc9/0m1MRbKg8bwp6CjLkrTmEPur9pQhSp4ylkZfyiyU4ZK0ncVc8cTQicQ9h8F5VcdAeBNhBnqHUR2JZLX7yK53GKPfIQNVxovKLXLKTUnLNyt7Et96NTIFvnIfo3KCWfjlXsFHj5lFu3MsaqDcq1zOJtMUWm8MMha5wXFV550FUOYw8fX6cFgtDc3TdSVpeNeFR49ErVN63GpZ0zKqRVAjotbMBkC1xjaAqzW5mR+1hjfzqdb8Zv5VjNDoi4opGv1SIYhWRxWxNNo7n1XSRESNdagAShuTCre06anorLFUFc01lq2iv8YTqGix8Rwqumw8jYpGG8+kotfGk42xbuP3VGTc+EkVSTd+VUXejR/Wkbr225fow1bv3jcd67K0ZxenNzLoR499vzfVCaGS2aV+w8RaJC8FHjDAyIosaxNw8bl/NmBFZ1suRMNKnsuhHWYC0xFDyfYxnVw9mgoZ8EiIKqvY6W3YSUNFS/e1StW5PpoMg8J0BDoqtojFAtnSOrsOQXIdBDhXsoXqgCU9yUpF/FHLJtU2g2wKuRNROIQOdlk2E+pZuZFVLuBs2cJ0YWUSxbWDkFOjJEVjasTBzcmmqTrpyc2hpvhWgNUgmslQQ1ZTp6RTszyjESXp6YtW/Qs78Suqr39Dqb6He5AbOZNX5GCkOFCKMTR+Qk3Mcnlog3aQK0oSdglWTY0Q0+l14yxqqpryhjzqh+Y7qpIehNY7PeSqpVq6UaEb7Kryi8+U7u/BNc/K9Z9GfHPD1kvDT7kBtRmE0LF8QGfUiMWjnwvXUHX+o5uBTfMdEdaD0NOhh1wnT0s3zvOsTmyp/KmcNAE+FkuApjtEIcGXfxSjcDDWO/h90xfJ3YbrqXhdPX249vShdUxq8dCO243dUBrv5mafHpnc3FuK5ecBXIIhgtKlbQH3SS4Y71+rXRZCsBNZAa6fVoDrp88Bv0Vx5YVs8Esp3gBlJlH8zYVEcSnJvEO2efu44nSFf10JptWU01vVxo1PUbd60DWes3//O0Qj2AundDptv8bgtHviki0jv//1H//x+M3b98fnzz5+eHbz2+PP377+aayu/NPh/wCh0kELCmVuZHN0cmVhbQplbmRvYmoKMTEgMCBvYmoKNjYwNgplbmRvYmoKMTYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA5MCA+PgpzdHJlYW0KeJw9jLENwDAIBHumYIFIgAHjfaJU9v5tCHHS8Kc/9B6KhIdJXmfDLgNPhuZRuECDiiY8mjKNpVJDkKMnsekm41Lv3vxn8pkUvUkO8hgoXp33j7adcN3aehvwCmVuZHN0cmVhbQplbmRvYmoKMTcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4OCA+PgpzdHJlYW0KeJw9jbkRwDAIBHOqoASBeKR+PI7k/lOf8BMAO+zcXLpyY02sVMdMPoQkZuFFGqNokUpj6w3k+D0UGq/9wrCj83Y2rK6joVuCZNpHyG1XveuvW3TeyQsbzgplbmRzdHJlYW0KZW5kb2JqCjE4IDAgb2JqCjw8IC9CQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzMgovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxNkktuazEMQ+d3FdpAAetvr6dAR3n7n74j3w4KJKBiSyRF50mTCPn3qC1RS/k8miXqLXpclDtzvfj9WJz3ZNPrS9xCdM2N95Iu8XOkXELXwPcT8f7eKXxSNxKH8wwoSyUTiX0ums7ErTIkw8QwkGbiSMF14O+GbAT2iznit9ol05Hwz0xu5aaspPDweWphCau5W7LsRfpQ3MPZMh0R9NvssWc6XLw4ISPXc9Hy3kxlzHCqDRs+zrWCZVjDXL7YxyMvEhDdU9lpWbCk2E1UCYEwcUtOyvfmpm5THDKbleSmr63SmryVrZJ2yKKlf4MaRMbfyhv0IKhkZiwHkr2ggrSGmBceJIB+q6KviajySF93E1TxVJ8ndYJRiZ4+WPxcRBHtqRybxX/IFTav2W3bGxkMVSw5GjVPqflWirti/Z617c+Kn+fnP7Yqe/EKZW5kc3RyZWFtCmVuZG9iagoxOSAwIG9iago8PCAvQkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA1MzIKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicPZNLbiYxCIT3fQpfYCQDBtvniTSrP/ffzld0MosWtHm6qvyU1/hjMb6fvHesHHlq2LTXZoyvp717OPHhUSN3Dq9SpHyEz5ErRqw90nZbIvM9WdTEmjRWpmrixnC6fV6PSa9nsUbsGscoiLE0OeYdmnV7RffV9uuxfdqzYCu2zTd9m6qTE79tjlah2k6Ms4Zt3DmxqSbygiybfWELG7u7pwkI44cju1vm63EuiuPLFfWKN9vprXK/DOCmbc9VBC8tuV97FCi3lItfMZVDt8ozHOSKfnZOW7Yoe09id4ZZ/dTcpImPA1e6MSY0Ts6sQXQBo9LXOmoEZcu4eUHDzB4hy3ADck4/DMv2zEXCHRcErHmEQpBcwApcMikscLQC0YJksus0pJRvZ2fabW6mAbKMQi/yxKgyRPFbEyhD94y8o6QnaitVs+qMPbVeuqrgGt63KruvUCpFdMK3Qb9Ydkc17XhQtoUbuLf1bJmgYVjdgCBWtEd6d+NPii14XtLzfxzKZnvlAo9NF0DdrmFiILsShCn2iIADESTnfHVnq6btnL0bUCuXLcy4k0GnApvhhrA/z5laDOf3gfJKWj2XpxroK8+7QUJCW98/rytSmAm9OFKfNLhQhqhbvLJEHoqyB9skeizmp3Qmu9/7si+TlVFZXVPViqCySu8LFNBfrtcS8fOeqKOQVGZL8Hfzz/P3H4io1HUKZW5kc3RyZWFtCmVuZG9iagoyMCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE0NCA+PgpzdHJlYW0KeJw9jzsSAyEMQ3tOoSPgP5xnM6k292+jJZAGv7GwJVsoOnLw8Rqo7HhJO/hpnk41cDdjb5PHIlNBsmu9kBm4mk5FcqMOKjqh5Yi5FO4JL0676Cabk6YPacgmiSfK3fJXJI9QsWGMPS51VgrtYkWTaUinsTAijdUTxZgMwOHib9Ncpxl/PvX6H3u39xdMuDPWCmVuZHN0cmVhbQplbmRvYmoKMjEgMCBvYmoKPDwgL0JCb3ggWyAtMTAxNiAtMzUxIDE2NjAgMTA2OCBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTgxCi9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nDVQOQ4EIQzreYU/sBK5w3tG2mr2/+2GMFOgGBwHO4NJ8SHBb0Q2kIkUeILDcY1kiDGIDaoCWg7TKIKXNLoHv1xq9RIoZomlekhLKXVc4QyW2OUaMvsupiBdkAxIDbmGlnSje6gcTm3CCUZ5pLbmBq6zJpfPNrr/8nZK8Ih244WP09B8nEZl3FykdaoIemJGzco9NnoJRty1HLGctdRSpFSLOlFlsNUPczb/7vEa3z/mNz8eCmVuZHN0cmVhbQplbmRvYmoKMjIgMCBvYmoKPDwgL0JCb3ggWyAtMTAxNiAtMzUxIDE2NjAgMTA2OCBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjUwCi9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nD1QSY4DMQi8+xV8IJILMMbvaSmnzP+vU9hOpG6B2WppHlNmdPlrriljpHyaL93ZcEYzGTPE0+RpgS5uKoEUC8auorM6I13AmeEpgIkvl6iGO4RvS5UXIIa549N0LnlpnwRE/lIli+qzGGejrvHLfu+NXbG4cBd/YhMCjxTBWj6UFb5F1FiJMjsyn2Yzt3QKviZ8mnEykm5YrEq8E9l5slBryVnHGNTHkwQb/K8DWOc4htiiT4tTunfKv4A4vXGCOnTH5wtH2f7FVds9ljJ2pkP3tiruPeRBAKuFCF+XA2hLsYL3zbImDm/QbQrRHoVz4Z72/gcRKWAACmVuZHN0cmVhbQplbmRvYmoKMjMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MSA+PgpzdHJlYW0KeJw1jMENwDAIA/9MwQKVAsGhA1V9Jft/a6HywDpZ5uDQoZczEJOX+piYrcIjXW6Bp8YCyQyaTgg0hFGwpTwcTL2rpjyyXoY3/eot7weyfxe0CmVuZHN0cmVhbQplbmRvYmoKMTQgMCBvYmoKPDwgL0Jhc2VGb250IC9EZWphVnVTYW5zLU9ibGlxdWUgL0NoYXJQcm9jcyAxNSAwIFIKL0VuY29kaW5nIDw8IC9EaWZmZXJlbmNlcyBbIDY1IC9BIDcyIC9IIDEwMiAvZiAxMjIgL3ogXSAvVHlwZSAvRW5jb2RpbmcgPj4KL0ZpcnN0Q2hhciAwIC9Gb250QkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZvbnREZXNjcmlwdG9yIDEzIDAgUgovRm9udE1hdHJpeCBbIDAuMDAxIDAgMCAwLjAwMSAwIDAgXSAvTGFzdENoYXIgMjU1IC9OYW1lIC9EZWphVnVTYW5zLU9ibGlxdWUKL1N1YnR5cGUgL1R5cGUzIC9UeXBlIC9Gb250IC9XaWR0aHMgMTIgMCBSID4+CmVuZG9iagoxMyAwIG9iago8PCAvQXNjZW50IDkyOSAvQ2FwSGVpZ2h0IDAgL0Rlc2NlbnQgLTIzNiAvRmxhZ3MgOTYKL0ZvbnRCQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRm9udE5hbWUgL0RlamFWdVNhbnMtT2JsaXF1ZQovSXRhbGljQW5nbGUgMCAvTWF4V2lkdGggMTM1MCAvU3RlbVYgMCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL1hIZWlnaHQgMCA+PgplbmRvYmoKMTIgMCBvYmoKWyA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMAo2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDMxOCA0MDEgNDYwIDgzOCA2MzYKOTUwIDc4MCAyNzUgMzkwIDM5MCA1MDAgODM4IDMxOCAzNjEgMzE4IDMzNyA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2CjYzNiA2MzYgMzM3IDMzNyA4MzggODM4IDgzOCA1MzEgMTAwMCA2ODQgNjg2IDY5OCA3NzAgNjMyIDU3NSA3NzUgNzUyIDI5NQoyOTUgNjU2IDU1NyA4NjMgNzQ4IDc4NyA2MDMgNzg3IDY5NSA2MzUgNjExIDczMiA2ODQgOTg5IDY4NSA2MTEgNjg1IDM5MCAzMzcKMzkwIDgzOCA1MDAgNTAwIDYxMyA2MzUgNTUwIDYzNSA2MTUgMzUyIDYzNSA2MzQgMjc4IDI3OCA1NzkgMjc4IDk3NCA2MzQgNjEyCjYzNSA2MzUgNDExIDUyMSAzOTIgNjM0IDU5MiA4MTggNTkyIDU5MiA1MjUgNjM2IDMzNyA2MzYgODM4IDYwMCA2MzYgNjAwIDMxOAozNTIgNTE4IDEwMDAgNTAwIDUwMCA1MDAgMTM1MCA2MzUgNDAwIDEwNzAgNjAwIDY4NSA2MDAgNjAwIDMxOCAzMTggNTE4IDUxOAo1OTAgNTAwIDEwMDAgNTAwIDEwMDAgNTIxIDQwMCAxMDI4IDYwMCA1MjUgNjExIDMxOCA0MDEgNjM2IDYzNiA2MzYgNjM2IDMzNwo1MDAgNTAwIDEwMDAgNDcxIDYxNyA4MzggMzYxIDEwMDAgNTAwIDUwMCA4MzggNDAxIDQwMSA1MDAgNjM2IDYzNiAzMTggNTAwCjQwMSA0NzEgNjE3IDk2OSA5NjkgOTY5IDUzMSA2ODQgNjg0IDY4NCA2ODQgNjg0IDY4NCA5NzQgNjk4IDYzMiA2MzIgNjMyIDYzMgoyOTUgMjk1IDI5NSAyOTUgNzc1IDc0OCA3ODcgNzg3IDc4NyA3ODcgNzg3IDgzOCA3ODcgNzMyIDczMiA3MzIgNzMyIDYxMSA2MDgKNjMwIDYxMyA2MTMgNjEzIDYxMyA2MTMgNjEzIDk5NSA1NTAgNjE1IDYxNSA2MTUgNjE1IDI3OCAyNzggMjc4IDI3OCA2MTIgNjM0CjYxMiA2MTIgNjEyIDYxMiA2MTIgODM4IDYxMiA2MzQgNjM0IDYzNCA2MzQgNTkyIDYzNSA1OTIgXQplbmRvYmoKMTUgMCBvYmoKPDwgL0EgMTYgMCBSIC9IIDE3IDAgUiAvZiAyMCAwIFIgL3ogMjMgMCBSID4+CmVuZG9iagoyOCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI1OSA+PgpzdHJlYW0KeJw9UklywzAMu/sVfAJ3Se9Jpyfn/9cC9NSXEGOKAAimd4vK2fhpK1l+5McuO0sit3wHbZP7iqoHpG6CzCXHJVeIWcrnSpBYtJSZWJ+pDsrPNahV+MJPzExMhyQRS8hJPYqwfl4H96B+vaTzW2T8o2OD0luSTAWdGu6Vo5TYsFSfGuQeNN2UVp+ZdmUHLI03ZKUmdfr10+MHSzClLxLRQYjEn+RyhywLKQfxdq7eQHhXuyDVUysPO0Saj5HeUgWrOTMBS0bTDiNgbdaYIFUCvEVrCLQW4vKFTisiPjk3dDBNVZ6FyLBS4Vh7z2gNF7qGvNJwepJx//kfvCve1+8f2vNmZAplbmRzdHJlYW0KZW5kb2JqCjI5IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjMyID4+CnN0cmVhbQp4nDVRO3IFMQjrfQpdIDPmb59nM69K7t9GsJNmYQEJCec92IjElxjSHeWKb1mdZhl+J4u8+FkpnLwXUYFURVgh7eBZzmqGwXMjU+ByJj7LzCfTYscCqok4zo6cZjAIMY3raDkdZpoHPSHXByNu7DTLVQxpvVuq1/da/lNF+ci6m+XWKZtaqVv0jD2Jy87rqS3tC6OO4qYg0uFjh/cgX8ScxUUn0s1+M+WwkjQEpwXwIzGU6tnhNcLEz4wET9nT6X2Uhtc+aLq+dy/oyM2ETOUWykjFk5XGmDFUvxHNJPX9P9CzPn+aMFRHCmVuZHN0cmVhbQplbmRvYmoKMzAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA3NyA+PgpzdHJlYW0KeJwzNzVSMFCwtAASZqYmCuZGlgophlxAPoiVy2VoaQ5m5YBZJsYGQJapqSkSCyIL0wthweRgtLGJOdQEBAskB7Y2B2ZbDlcaAJ7gG5oKZW5kc3RyZWFtCmVuZG9iagozMSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIxMiA+PgpzdHJlYW0KeJw1UDkOAzEI7P2K+UAkg20w79koXf7fhgGlWDFa5sJ+HRPH8JIFXwLfireMFRtmiu9YqoXUDmwdqC6cq3iGXMHRC7GJnRacyzY3idQVZEhEaWRbbugSijZFp+TvTXNLN+X2pEnTbVoZmHoZcnYEEUPJYAlquhZNWLQ9Ff9TnjqK933HDit03OHTkx/1PcNnPodLvcX2qNmJRLovyJDTmksJTTTZ0a/IFM48NqSQziBBUlyCa2WQ7emXowMSMDG3LEB2V6KcJWnH0v8znvH5AQHbU6kKZW5kc3RyZWFtCmVuZG9iagozMiAwIG9iago8PCAvQkJveCBbIC0xMDIxIC00NjMgMTc5NCAxMjMzIF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMzcKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicPVG7ccUwDOs9BUbgR/xonneXKtm/DSg5KXiAKREE5Kcs0YWfZ4jg+1nu/8gDkq1QbYQnNBWRDdPA50kRWG6kJtxe3OeEbJUj9uJcIMIQ7TwJaaQLFjsZC94XP4+rHmasuWH8vjOafVR01VEdvHsO42ZNP06U3evNrI5bm/t0764Th2tIJp/3H5yUSqeXLIM6S7iwNpoa1uO8KMZYzDj+J6qwTbK2owrB0iVIKtCAGEoSxoDFLf4iJ1oOC9qbG2nrnclOqjSKhhejDN6g9UY4inSRfJhrK4OxqZg2vvnkJTfo+2e/n69fA2ta6wplbmRzdHJlYW0KZW5kb2JqCjMzIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjI3ID4+CnN0cmVhbQp4nEWQS44DIRBD95zCR6D+cJ6OsurcfzsuOtFssCUo1zO5AxN78chMlG68ZLg7zBWf4Rkwc/hKmGzETOhOXCOUrhThVJ8IjsvevOmgiXtEzqOeBVnVzg1qAWeS5oLtgi7njBU3zsmtRuXN9KPXEL5pdx/XeYf2SOPew1S+zjnVzruKCGkLWdW0vpBsFMkOaz8qTdvOyxCx4GwaVugc3gi7V3cnSxh+v/IwJRM/D936UXxdN6PrFGcnVyZrz3noSelf9cqjD8VxKegXse3MJPdfp1OSqVN7Z+9p/ae4x/sPkG5WOQplbmRzdHJlYW0KZW5kb2JqCjM0IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzA0ID4+CnN0cmVhbQp4nD2SO5LDMAxDe52CF8iM+JPk82Qnlff+7T4yyVaASYkAKC91mbKmPCBpJgn/0eHhYjvld9iezczAtUQvE8spz6ErxNxF+bKZjbqyOsWqwzCdW/SonIuGTZOa5ypLGbcLnsO1ieeWfcQPNzSoB3WNS8IN3dVoWQrNcHX/O71H2Xc1PBebVOrUF48XURXm+SFPoofpSuJ8PCghXHswRhYS5FPRQI6zXK3yXkL2DrcassJBaknnsyc82HV6Ty5uF80QD2S5VPhOUezt0DO+7EoJPRK24VjufTuasekamzjsfu9G1sqMrmghfshXJ+slYNxTJkUSZE62WG6L1Z7uoSimc4ZzGSDq2YqGUuZiV6t/DDtvLC/ZLMiUzAsyRqdNnjh4yH6NmvR5led4/QFs83M7CmVuZHN0cmVhbQplbmRvYmoKMzUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA1NCA+PgpzdHJlYW0KeJwzNjZXMFAwNDJX0DUyNlUwMjRQMDczUUgx5IIxc8EssGwOF1whhAmSz4GrzOFKAwBMkA8VCmVuZHN0cmVhbQplbmRvYmoKMzYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNzkgPj4Kc3RyZWFtCnicPVI7ksUgDOtzCl+AGfAXzpOdrbL3b1eCvFdkrERGkh3SUroMDWkjVWIMqezyMy7CtlT+DiL7XD6/0NY60JyHo4uNCaAp96WrA3YVrZIWvusoMgTmENhommhOUXAKCbV92nCQh/oA6zIidr0vBiV6NrKtQ/Yg9hOpGVJBOfCOhFCEh82+Y/g4cTztzRNgTp4MOCN79TNOKV05YTkUMDK3wy2w3tdnX89GuYi85gdhDiLHInJiUxMMkkCxHF6OdPDUU6M2A+RRXDBRx2yxwM+9Zz7oMaRT6JHt2FwupF5k8IX52aHwYD+3AAYqqrWdBjtYvb+OY72GDb+P4VrkjtuKLRygTRcOxDvBEVnv7y15rt9/B3JuBgplbmRzdHJlYW0KZW5kb2JqCjM3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjc2ID4+CnN0cmVhbQp4nD1SS47oMAjb5xRcIFL4Jj1PR7Pqu//22bSaFRZgY0jKS5aopUwtk1SVXUt+dHTuMvk3NK9Gz7D15sxD5kmxODK3yj0M5JlbrNBrb9SrCwCxSO7UEtslxpZLxZJkh6ztEHdk0OHFKtnM+NrCDjdrjkdSFypepwcF+Yww8E7Mfb6JZSE0Vxltt8BBDxaoAz0wCxO5IuPdaxM9jXgLoKwPmb+ILjfUXI9sTIBTuNoL3qmU1jEPFYmiHOxGGr2fo+Y4ocPbPWI59nIJRwbe4mjHe/BFiJ5GVkSsfsizEfmGDalIj5jKG+puH3r8ja3YaH92JknB11/W20w10rng1Fyt1l+DR2jw3qjh8/dLnvH7HyEmbhIKZW5kc3RyZWFtCmVuZG9iagozOCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIzMCA+PgpzdHJlYW0KeJw1UUluwzAMvOsV84EA4i6/x0FP7f+vHdIJYGBoS5zNERsbEXiJwc9B5MZb1oya+JvJXfG7PBUeCbeCJ1EEXoZ72QkubxiX/TjMfPBeWjmTGk8yIBfZ9PBEyGCXQOjA7BrUYZtpJ/qGhM+OSDUbWU5fS9BLqxAoT9l+pwtKtK3qz+2zLrTta0842e2pJ5VPIJ5bsgKXjVdMFmMZ9ETlLsX0QaqzhZ6E8qJ8DrL5qCESXaKcgScGB6NAO7Dntp+JV4WgdXWfto2hGikdT/82NDVJIuQTJZzZ0rhb+P6ee/38A6ZUU58KZW5kc3RyZWFtCmVuZG9iagozOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDY4ID4+CnN0cmVhbQp4nDM2NlcwUDA0BJFGRgYKpkBWiiEXSMDQyEQhlwskCGLlgFkGQBqiOAeuBsICaYSoBrEgqo0tjaGyCBZENg0AR6IWywplbmRzdHJlYW0KZW5kb2JqCjQwIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNjYgPj4Kc3RyZWFtCnicMza0UDBQMDdX0DU0NFUwMjJQMDQyUUgx5DI0NAczc7lggjlglokBkGEIJMEacrhgWnPAOiCyUK05XGkATTgR9QplbmRzdHJlYW0KZW5kb2JqCjQxIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjI3ID4+CnN0cmVhbQp4nDVPO7IDIQzrOYUukBmMbWDPs5lUL/dvn2SyDRL+SPL0REcmXubICKzZ8bYWGYgZ+BZT8a897cOE6j24hwjl4kKYYSScNeu4m6fjxb9d5TPWwbsNvmKWFwS2MJP1lcWZy3bBWBoncU6yG2PXRGxjXevpFNYRTCgDIZ3tMCXIHBUpfbKjjDk6TuSJ52KqxS6/72F9waYxosIcVwVP0GRQlj3vJqAdF/Tf1Y3fSTSLXgIykWBhnSTmzllO+NVrR8dRiyIxJ6QZ5DIR0pyuYgqhCcU6OwoqFQWX6nPK3T7/aF1bTQplbmRzdHJlYW0KZW5kb2JqCjQyIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjQ1ID4+CnN0cmVhbQp4nEVQu41DMQzrPQUXCGD9LHued0iV2789SkZwhSFaP5JaEpiIwEsMsZRv4kdGQT0LvxeF4jPEzxeFQc6EpECc9RkQmXiG2kZu6HZwzrzDM4w5AhfFWnCm05n2XNjknAcnEM5tlPGMQrpJVBVxVJ9xTPGqss+N14GltWyz05HsIY2ES0klJpd+Uyr/tClbKujaRROwSOSBk0004Sw/Q5JizKCUUfcwtY70cbKRR3XQydmcOS2Z2e6n7Ux8D1gmmVHlKZ3nMj4nqfNcTn3usx3R5KKlVfuc/d6RlvIitduh1elXJVGZjdWnkLg8/4yf8f4DjqBZPgplbmRzdHJlYW0KZW5kb2JqCjQzIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzkyID4+CnN0cmVhbQp4nD1SS24FMQjbzym4QKXwTXKeqd7u3X9bm8xUqgovA7YxlJcMqSU/6pKIM0x+9XJd4lHyvWxqZ+Yh7i42pvhYcl+6hthy0ZpisU8cyS/ItFRYoVbdo0PxhSgTDwAt4IEF4b4c//EXqMHXsIVyw3tkAmBK1G5AxkPRGUhZQRFh+5EV6KRQr2zh7yggV9SshaF0YogNlgApvqsNiZio2aCHhJWSqh3S8Yyk8FvBXYlhUFtb2wR4ZtAQ2d6RjREz7dEZcVkRaz896aNRMrVRGQ9NZ3zx3TJS89EV6KTSyN3KQ2fPQidgJOZJmOdwI+Ge20ELMfRxr5ZPbPeYKVaR8AU7ygEDvf3eko3Pe+AsjFzb7Ewn8NFppxwTrb4eYv2DP2xLm1zHK4dFFKi8KAh+10ETcXxYxfdko0R3tAHWIxPVaCUQDBLCzu0w8njGedneFbTm9ERoo0Qe1I4RPSiyxeWcFbCn/KzNsRyeDyZ7b7SPlMzMqIQV1HZ6qLbPYx3Ud577+vwBLgChGQplbmRzdHJlYW0KZW5kb2JqCjQ0IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNzEgPj4Kc3RyZWFtCnicszC2UDBQMDQwUzA0N1IwNzZSMDE1UUgx5AIJgZi5XDDBHDDLGKgsByyLYEFkQSwjU1OoDhALosMQrg7BgsimAQDr5xgyCmVuZHN0cmVhbQplbmRvYmoKNDUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzMgPj4Kc3RyZWFtCnicTY9BEsMwCAPvfoWegLEB8550ekr+fy2QNu4F7YyAkYYwCDxiDOswJbx6++FVpEtwNo75JRlFPAhqC9wXVAVHY4qd+Njdoeyl4ukUTYvrEXPTtKR0N1Eqbb2dyPjAfZ/eH1W2JJ2CHlvqhC7RJPJFAnPYVDDP6sZLS4+n7dneH2Y+M9cKZW5kc3RyZWFtCmVuZG9iago0NiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0NyA+PgpzdHJlYW0KeJxNUbttRDEM698UXOAA62t5ngtSXfZvQ8kIkMIgoS8ppyUW9sZLDOEHWw++5JFVQ38ePzHsMyw9yeTUP+a5yVQUvhWqm5hQF2Lh/WgEvBZ0LyIrygffj2UMc8734KMQl2AmNGCsb0kmF9W8M2TCiaGOw0GbVBh3TRQsrhXNM8jtVjeyOrMgbHglE+LGAEQE2ReQzWCjjLGVkMVyHqgKkgVaYNfpG1GLgiuU1gl0otbEuszgq+f2djdDL/LgqLp4fQzrS7DC6KV7LHyuQh/M9Ew7d0kjvfCmExFmDwVSmZ2RlTo9Yn23QP+fZSv4+8nP8/0LFShcKgplbmRzdHJlYW0KZW5kb2JqCjQ3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggOTAgPj4Kc3RyZWFtCnicTY1BEsAgCAPvvCJPUETQ/3R60v9fq9QOvcBOAokWRYL0NWpLMO64MhVrUCmYlJfAVTBcC9ruosr+MklMnYbTe7cDg7LxcYPSSfv2cXoAq/16Bt0P0hwiWAplbmRzdHJlYW0KZW5kb2JqCjQ4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzM4ID4+CnN0cmVhbQp4nEVSS3LFMAjb5xRcIDPmZ+PzvE5X6f23lXA63Tz0DAgJMj1lSKbcNpZkhOQc8qVXZIjVkJ9GjkTEEN8pocCu8rm8lsRcyG6JSvGhHT+XpTcyza7QqrdHpzaLRjUrI+cgQ4R6VujM7lHbZMPrdiHpOlMWh3As/0MFspR1yimUBG1B39gj6G8WPBHcBrPmcrO5TG71v+5bC57XOluxbQdACZZz3mAGAMTDCdoAxNza3hYpKB9VuopJwq3yXCc7ULbQqnS8N4AZBxg5YMOSrQ7XaG8Awz4P9KJGxfYVoKgsIP7O2WbB3jHJSLAn5gZOPXE6xZFwSTjGAkCKreIUuvEd2OIvF66ImvAJdTplTbzCntrix0KTCO9ScQLwIhtuXR1FtWxP5wm0PyqSM2KkHsTRCZHUks4RFJcG9dAa+7iJGa+NxOaevt0/wjmf6/sXFriD4AplbmRzdHJlYW0KZW5kb2JqCjQ5IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTYzID4+CnN0cmVhbQp4nEWQuXUEMQxDc1WBEniAOuoZP0ez/acLabzeQPp4hHiIPQnDcl3FhdENP962zDS8jjLcjfVlxviosUBO0AcYIhNXo0n17YozVOnh1WKuo6JcLzoiEsyS46tAI3w6ssdDW9uZfjqvf+wh7xP/KirnbmEBLqruQPlSH/HUj9lR6pqhjyorax5q2r8IuyKUtn1cTmWcunsHtMJnK1f7fQOo5zqACmVuZHN0cmVhbQplbmRvYmoKNTAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA1MiA+PgpzdHJlYW0KeJwzNjNUMFAwsVQwMjZRMDY0AmIThRRDLqAIiJXLBRPLAbNAqnK4oMpzYKpyuNIA6QkNwAplbmRzdHJlYW0KZW5kb2JqCjUxIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNjggPj4Kc3RyZWFtCnicMzK3UDBQsDQBEoYWJgrmZgYKKYZcQL6piblCLhdIDMTKAbMMgLQlnIKIW0I0QZSCWBClZiZmEEk4AyKXBgDJtBXlCmVuZHN0cmVhbQplbmRvYmoKNTIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MSA+PgpzdHJlYW0KeJw9zLsVgDAIBdA+U7wRQnyA7OOx0v1bwUQbuHzVAx0hGdQNbh2HtKxLd5N96nq1iaTIgNJTalwaToyoaX2pfWrguxvmS9WJP83P5wOHxxlrCmVuZHN0cmVhbQplbmRvYmoKNTMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA0NSA+PgpzdHJlYW0KeJwzMrdQMFCwNAEShhYmCuZmBgophlyWEFYuF0wsB8wC0ZZwCiKeBgCffQy1CmVuZHN0cmVhbQplbmRvYmoKNTQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNTUgPj4Kc3RyZWFtCnicRZFLkgMgCET3noIjgPzkPJmaVXL/7TSYTDZ2l6j9hEojphIs5xR5MP3I8s1ktum1HKudjQKKIhTM5Cr0WIHVnSnizLVEtfWxMnLc6R2D4g3nrpxUsrhRxjqqOhU4pufK+qru/Lgsyr4jhzIFbNY5DjZw5bZhjBOjzVZ3h/tEkKeTqaPidpBs+IOTxr7K1RW4Tjb76iUYB4J+oQlM8k2gdYZA4+YpenIJ9vFxu/NAsLe8CaRsCOTIEIwOQbtOrn9x6/ze/zrDnefaDFeOd/E7TGu74y8xyYq5gEXuFNTzPRet6wwd78mZY3LTfUPnXLDL3UGmz/wf6/cPUIpmiAplbmRzdHJlYW0KZW5kb2JqCjU1IDAgb2JqCjw8IC9CQm94IFsgLTEwMjEgLTQ2MyAxNzk0IDEyMzMgXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDM3Ci9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nOMyNDBTMDY1VcjlMjc2ArNywCwjcyMgCySLYEFk0wABXwoKCmVuZHN0cmVhbQplbmRvYmoKNTYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNjEgPj4Kc3RyZWFtCnicRZBLEsMgDEP3nEJH8EcGfJ50ukrvv60hTbOAp7FABncnBKm1BRPRBS9tS7oLPlsJzsZ46DZuNRLkBHWAVqTjaJRSfbnFaZV08Wg2cysLrRMdZg56lKMZoBA6Fd7touRypu7O+Udw9V/1R7HunM3EwGTlDoRm9SnufJsdUV3dZH/SY27Wa38V9qqwtKyl5YTbzl0zoATuqRzt/QWpczqECmVuZHN0cmVhbQplbmRvYmoKNTcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMjAgPj4Kc3RyZWFtCnicNVG7ccUwDOs1BRfwnfiVNI9zr8rbvw1AOxVhGgRAqrxkSrlc6pJVssLkR4fqFE35PmCm/A71kOPoHtkhulPWlnsYCMvEPKWOWE2We7gFgS8MTYm5hfP3COgrBqMwE4G6xd8/QLMkMGlw8FOQa61aYokOPCwWWLMrzK0aKVTIVXw7NrkHBXJxs9CnHJoUt9yC8GWIZEdqsa/LZSnyu/UJGIQV5ohPFImF54EOZiLxJwNie/bZYldXL6oRGdZJhwdSBNJsbhIwNEWy6oMb2FfHNT9PR9nByUG/isH4NjiZL0l5XwWhEI8X/g7P2cixkkMkFPJ9tcCII2yAEaFP7SMQZSA0RffumVI+JlWK7wBGIRx9qlcyvBeR2WqGzf8ZXdkqCgZVWR+fRnAmg0k482SjCtNStdO/+9zj8wdjY3qACmVuZHN0cmVhbQplbmRvYmoKNTggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMTQgPj4Kc3RyZWFtCnicPVC7EUMxCOs9BQvkznztN8/Lpcv+bSScpEI2QhKUmkzJlIc6ypKsKU8dPktih7yH5W5kNiUqRS+TsCX30ArxfYnmFPfd1ZazQzSXaDl+CzMqqhsd00s2mnAqE7qg3MMz+g1tdANWhx6xWyDQpGDXtiByxw8YDMGZE4siDEpNBv+tcvdS3O89HG+iiJR08K755fTLzy28Tj2ORLq9+YprcaY6CkRwRmryinRhxbLIQ6TVBDU9A2u1AK7eevk3aEd0GYDsE4njNKUcQ//WuMfrA4eKUvQKZW5kc3RyZWFtCmVuZG9iago1OSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDgwID4+CnN0cmVhbQp4nEWMuw3AMAhEe6ZgBH4mZp8olbN/GyBK3HBPunu4OhIyU95hhocEngwshlPxBpmjYDW4RlKNneyjsG5fdYHmelOr9fcHKk92dnE9zcsZ9AplbmRzdHJlYW0KZW5kb2JqCjYwIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjM2ID4+CnN0cmVhbQp4nE1QS25EIQzbc4pc4EkkIQHOQ9VV5/7bscNU7SqGGH9ID+myVR7rU2J1iezypU2XyjJ5FajlT9v/UQwCbv/QyEG0t4ydYuYS1sXCJDzlNCMbJ9csH487TxtmhcbEjeOdLhlgnxYBNVuVzYE5bTo3QLqQGreqs95kUAwi6kLNB5MunKfRl4g5nqhgSncmtZAbXD7VoQNxWr0KuWOLk2/EHFmhwGHQTHHWXwHWqMmyWcggSYYhzn2je5QKjajKeSsVwg+ToRH1htWgBpW5haKp5ZL8HdoCMAW2jHXpDEqBqgDB3yqnfb8BJI1dUwplbmRzdHJlYW0KZW5kb2JqCjYxIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTQ3ID4+CnN0cmVhbQp4nD1PuQ0DMQzrPQUXOMB6LFvzXJDqsn8bykZSCCJA8ZFlR8cKXGICk445Ei9pP/hpGoFYBjVH9ISKYVjgbpICD4MsSleeLV4MkdpCXUj41hDerUxkojyvETtwJxejBz5UG1keekA7RBVZrknDWNVWXWqdsAIcss7CdT3MqgTl0SdrKR9QVEK9dP+fe9r7CwBvL+sKZW5kc3RyZWFtCmVuZG9iago2MiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE0OSA+PgpzdHJlYW0KeJw1j0sOAyEMQ/c5hS8wUn6EcB6qrqb33zZhWgkJC9svwRaDkYxLTGDsmGPhJVRPrT4kI4+6STkQqVA3BE9oTAwzbNIl8Mp03zKeW7ycVuqCTkjk6aw2GqKMZl7D0VPOCpv+y9wkamVGmQMy61S3E7KyYAXmBbU89zPuqFzohIedyrDoTjGi3GZGGn7/2/T+AnsyMGMKZW5kc3RyZWFtCmVuZG9iago2MyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDQ5ID4+CnN0cmVhbQp4nDM2tFAwUDA0MAeSRoZAlpGJQoohF0gAxMzlggnmgFkGQBqiOAeuJocrDQDG6A0mCmVuZHN0cmVhbQplbmRvYmoKNjQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNTcgPj4Kc3RyZWFtCnicRZC5EUMxCERzVUEJErAI6rHH0Xf/qRf5SrRvAC2HryVTqh8nIqbc12j0MHkOn00lVizYJraTGnIbFkFKMZh4TjGro7ehmYfU67ioqrh1ZpXTacvKxX/zaFczkz3CNeon8E3o+J88tKnoW6CvC5R9QLU4nUlQMX2vYoGjnHZ/IpwY4D4ZR5kpI3Fibgrs9xkAZr5XuMbjBd0BN3kKZW5kc3RyZWFtCmVuZG9iago2NSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzMiA+PgpzdHJlYW0KeJwtUjmOJDEMy/0KfmAA6/Lxnh5M1Pv/dElVBQWqbMs85HLDRCV+LJDbUWvi10ZmoMLwr6vMhe9I28g6iGvIRVzJlsJnRCzkMcQ8xILv2/gZHvmszMmzB8Yv2fcZVuypCctCxosztMMqjsMqyLFg6yKqe3hTpMOpJNjji/8+xXMXgha+I2jAL/nnqyN4vqRF2j1m27RbD5ZpR5UUloPtac7L5EvrLFfH4/kg2d4VO0JqV4CiMHfGeS6OMm1lRGthZ4OkxsX25tiPpQRd6MZlpDgC+ZkqwgNKmsxsoiD+yOkhpzIQpq7pSie3URV36slcs7m8nUkyW/dFis0UzuvCmfV3mDKrzTt5lhOlTkX4GXu2BA2d4+rZa5mFRrc5wSslfDZ2enLyvZpZD8mpSEgV07oKTqPIFEvYlviaiprS1Mvw35f3GX//ATPifAEKZW5kc3RyZWFtCmVuZG9iago2NiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDY4ID4+CnN0cmVhbQp4nDMzNlMwULAwAhKmpoYK5kaWCimGXEA+iJXLBRPLAbPMLMyBLCMLkJYcLkMLYzBtYmykYGZiBmRZIDEgutIAcvgSkQplbmRzdHJlYW0KZW5kb2JqCjY3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzE3ID4+CnN0cmVhbQp4nDVSS3JDMQjbv1Nwgc6Yv32edLJq7r+thCcrsC1AQi4vWdJLftQl26XD5Fcf9yWxQj6P7ZrMUsX3FrMUzy2vR88Rty0KBFETPfgyJxUi1M/U6Dp4YZc+A68QTikWeAeTAAav4V94lE6DwDsbMt4Rk5EaECTBmkuLTUiUPUn8K+X1pJU0dH4mK3P5e3KpFGqjyQgVIFi52AekKykeJBM9iUiycr03VojekFeSx2clJhkQ3SaxTbTA49yVtISZmEIF5liA1XSzuvocTFjjsITxKmEW1YNNnjWphGa0jmNkw3j3wkyJhYbDElCbfZUJqpeP09wJI6ZHTXbtwrJbNu8hRKP5MyyUwccoJAGHTmMkCtKwgBGBOb2wir3mCzkWwIhlnZosDG1oJbt6joXA0JyzpWHG157X8/4HRVt7owplbmRzdHJlYW0KZW5kb2JqCjY4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNTIgPj4Kc3RyZWFtCnicMzY2VzAAQl1LIwVjINvcyFIhxZDLyNQEzMzlggnmcFkYg1XlcBlAaZiiHK40AN+qDa0KZW5kc3RyZWFtCmVuZG9iago2OSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE3ID4+CnN0cmVhbQp4nDM2tFAwgMMUQy4AGpQC7AplbmRzdHJlYW0KZW5kb2JqCjcwIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTMxID4+CnN0cmVhbQp4nEWPyw0EIQxD71ThEvIZPqmH1Z7Y/q/rMJpBQvhBIjvxMAis8/I20MXw0aLDN/421atjlSwfunpSVg/pkIe88hVQaTBRxIVZTB1DYc6YysiWMrcb4bZNg6xslVStg3Y8Bg+2p2WrCH6pbWHqLPEMwlVeuMcNP5BLrXe9Vb5/QlMwlwplbmRzdHJlYW0KZW5kb2JqCjcxIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzM4ID4+CnN0cmVhbQp4nDVSOa7dQAzrfQpdIIB2zZznBal+7t+GlF8KQ7RWipqOFpVp+WUhVS2TLr/tSW2JG/L3yQqJE5JXJdqlDJFQ+TyFVL9ny7y+1pwRIEuVCpOTksclC/4Ml94uHOdjaz+PI3c9emBVjIQSAcsUE6NrWTq7w5qN/DymAT/iEXKuWLccYxVIDbpx2hXvQ/N5yBogZpiWigpdVokWfkHxoEetffdYVFgg0e0cSXCMjVCRgHaB2kgMObMWu6gv+lmUmAl07Ysi7qLAEknMnGJdOvoPPnQsqL8248uvjkr6SCtrTNp3o0lpzCKTrpdFbzdvfT24QPMuyn9ezSBBU9YoaXzQqp1jKJoZZYV3HJoMNMcch8wTPIczEpT0fSh+X0smuiiRPw4NoX9fHqOMnAZvAXPRn7aKAxfx2WGvHGCF0sWa5H1AKhN6YPr/1/h5/vwDHLaAVAplbmRzdHJlYW0KZW5kb2JqCjcyIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjQ4ID4+CnN0cmVhbQp4nC1ROZIDQQjL5xV6QnPT77HLkff/6QrKAYOGQyA6LXFQxk8Qlive8shVtOHvmRjBd8Gh38p1GxY5EBVI0hhUTahdvB69B3YcZgLzpDUsgxnrAz9jCjd6cXhMxtntdRk1BHvXa09mUDIrF3HJxAVTddj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   "source": [
    "fc = 1000  # Hz\n",
    "B, A, b, a = audiofilter.biquad_hp1st(fc, fs)\n",
    "bode_plot(B, A, b, a)"
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    "<a id=\"highpass2nd\"></a>\n",
    "### 2nd Order Highpass `hp2nd`\n",
    "\n",
    "\\cite{TietzeSchenk2008}, \\cite{Moschytz1981}\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| $\\frac{1}{\\omega_\\text{c}^2}$ | 0 | 0 | $\\frac{1}{\\omega_\\text{c}^2}$ | $\\frac{\\text{a}_\\text{i}}{\\omega_\\text{c}}$ | $\\text{b}_\\text{i}$ |\n",
    "\n",
    "with cut frequency $\\omega_c$ in rad/s and filter characteristic coefficients $\\text{b}_\\text{i}$ and $\\text{a}_\\text{i}$ (see Appendix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [2.5330295910584447e-08 0.0000000000000000e+00 0.0000000000000000e+00]\n",
      "A = [2.5330295910584447e-08 2.2507907903927655e-04 1.0000000000000000e+00]\n",
      "b = [ 0.9115866680128314 -1.8231733360256628  0.9115866680128314]\n",
      "a = [ 1.                 -1.815341082704568   0.8310055893467575]\n"
     ]
    },
    {
     "data": {
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       "     <use x=\"887.158203\" xlink:href=\"#DejaVuSans-104\"/>\n",
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       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pd628d6b9d5\">\n",
       "   <rect height=\"157.5\" width=\"253.636364\" x=\"50.595312\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p46877ea045\">\n",
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       "   <rect height=\"253.636364\" width=\"253.636364\" x=\"354.958949\" y=\"68.749943\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fc = 1000  # Hz\n",
    "B, A, b, a = audiofilter.biquad_hp2nd(fc, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"bandpass2nd\"></a>\n",
    "### 2nd Order Bandpass `bp2nd`\n",
    "\n",
    "\\cite{TietzeSchenk2008}, \\cite{Moschytz1981}\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| 0 | $\\frac{1}{Q_\\text{BP}\\,\\omega_\\text{m}}$ | 0 | $\\frac{1}{\\omega_\\text{m}^2}$ | $\\frac{1}{Q_\\text{BP}\\,\\omega_\\text{m}}$ | 1 |\n",
    "\n",
    "with mid frequency $\\omega_m=2 \\pi f_m$ in rad/s and bandpass quality $Q_\\text{BP}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [0.                     0.00023873241463784307 0.                    ]\n",
      "A = [2.5330295910584447e-08 2.3873241463784307e-04 1.0000000000000000e+00]\n",
      "b = [ 0.08934001866587332  0.                  -0.08934001866587332]\n",
      "a = [ 1.                 -1.8057383179049802  0.8213199626682534]\n",
      "fcut_low = 500.0 Hz\n",
      "fmid = 1000 Hz\n",
      "fcut_high = 2000.0 Hz\n",
      "QBP = 0.6666666666666666\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BW = 2  # bandwidth in octaves\n",
    "fm = 1000  # Hz\n",
    "\n",
    "fcl = 2 ** (-BW / 2) * fm  # lower cut (-3 dB) frequency in Hz\n",
    "fch = 2 ** (+BW / 2) * fm  # higher cut (-3 dB) frequency in Hz\n",
    "QBP = audiofilter.q_from_bw(BW)\n",
    "np.testing.assert_allclose(QBP, fm / (fch - fcl))\n",
    "B, A, b, a = audiofilter.biquad_bp2nd(fm, QBP, fs)\n",
    "\n",
    "bode_plot(B, A, b, a)\n",
    "print(\"fcut_low =\", fcl, \"Hz\")\n",
    "print(\"fmid =\", fm, \"Hz\")\n",
    "print(\"fcut_high =\", fch, \"Hz\")\n",
    "print(\"QBP =\", QBP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"bandstop2nd\"></a>\n",
    "### 2nd Order Bandstop `bs2nd`\n",
    "\n",
    "\\cite{TietzeSchenk2008}, \\cite{Moschytz1981}\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "$\\frac{1}{\\omega_\\text{m}^2}$ | 0 | 1 | $\\frac{1}{\\omega_\\text{m}^2}$ | $\\frac{1}{Q_\\text{BS}\\,\\omega_\\text{m}}$ | 1 | \n",
    "\n",
    "with mid frequency $\\omega_m=2 \\pi f_m$ in rad/s and bandstop quality $Q_\\text{BS}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [2.5330295910584447e-08 0.0000000000000000e+00 1.0000000000000000e+00]\n",
      "A = [2.5330295910584447e-08 2.3873241463784307e-04 1.0000000000000000e+00]\n",
      "b = [ 0.9106599813341267 -1.8057383179049802  0.9106599813341267]\n",
      "a = [ 1.                 -1.8057383179049802  0.8213199626682534]\n",
      "fcut_low = 500.0 Hz\n",
      "fmid = 1000 Hz\n",
      "fcut_high = 2000.0 Hz\n",
      "QBS = 0.6666666666666666\n"
     ]
    },
    {
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G9VfyC4arbqSHS69h8t+hXW79wry9X+zO+dzJDJoRxtJaa4W7zGVmM03w8urcMU+DX0m5nlwW3NIyKbilN5cmNU/zaTBfTZJ1a3Z9FrxW6Q/8KKjKbbmHq209DdKqrNYMzCzci/aG2iMR7yttuYcLbT0N6LqgVlaheZLuhX1T8ZHAL4tsuY0aW0+EvaqlpSCapbux31J8KPaL+lpuo7zWE2GvymgpiGbpbuy3FB+K/aK0ltuorPVE2KsKWgqiWbob+y3Fh2K/qKrlHi6q9TTQ6+JZM0JKuhf6TcVHQr8sqOUerqf1RNCrulkKoVm6G/otxYdCv6il5R4upfVE0KuSWQqhWbob+i3Fh0K/KKPlNqpoPQ32a+u817fWeTtraN1YVh6J/aKCltsooPU02KtKWTNCs/BNkH+4fNaqWh9vHTp+GitVlay5ObNwr5Ubau9tpaqQNTdnFu61ckPt3a2cymOp1lxku218SOm9LdSFsdQcdZbutXJT8f0tnYti6QZN0v2Wbii+u6VzRSzVnkm4286H1d7dSlUMS7Vnlu62c0vx3S1VhbD0Gn6S7rZ0S/HdLVVFsFSDZuluS7cU39/SqQKWbs9FuN/OB9Xe3UpV/ErvgEzS3XZuKb63pbrwlVp6zdK9lm4qvrulquiVatAs3W3pluK7W6oKXqkGzdLdlm4pvr+lc7Er3aBJut/SDcV3t1QVulINmqW7Ld1SfH9L5yJXukGTdL+lG4p7Sw8sfFV/9mWv7pZEsJ7/8BPTCKbDxfmuDtFvfbnB8WBAV+uq3PHz0kU7lDjp8A7sSboPbKX0ArbWeAjYAC+0LKgGtl+tLPa0YOc01sPpwJ6k+8BWSi9ga43HFRXjkQxn5+pWB3g3j88I/XWAT9J9gCulF8C1xuMAr24opk4uHg7wcGvTWkGOWbwPcq32gnmn87gqKNa6zSJLT4w5Zja1XHH4LN6JuVI7Ya51HlaPw/K/ysTlh/h5ZAmGKyqfxTsxV2onzLXO4zBnE/PE5keQOc+/+njF5rN4J+ZK7YS51nl3Qo8XGucB4Tgl6b93yJxlXo+9lQ/Sa2on1LXOA1HnCWNV7meelqt6PxZLunMtXamfNESWLxlPPOhF3f1K+tzI+f/8Vi77vPq8cbDlT198aS9Z7D/V695yjSCLTmC9lSif1hGZTAhMz4cYfdhqMfA8b+K6G+Igx7/loHRlzZfAAgE8qlgSD1XwQLThkVxXfJC4XotLUgGCf1sdnKKK3FSmqFHusD43xkW+lUm7JkpVDuthEasX8FQ4zwTW3I7wAzUffazQY6ToT/WtjgGb6R1zy/iFzucsx2Bh6FDhsXyvjL0Y5WA1CxygDTzhbHnMtvoYRX/EUAqADu03LO9hx9PoiVND5vJCbliYo1W1kXyEnJKnK3ss/cdCA+iCkh2wxMTWsmJRqzMQIMaMPvD4YebBfpGWITvOqnnAyNhWaKE4jAWpwcOqJC4EJxrkVG/NUFzQGbmMrZ6O7ueK34P1LifrfZHaB3LEEYgvatlIZDTE89zOoMMQnjUnajx72k5TA2eY4DO6IgQ8UnMr9sHzej5YDvhghwS/Na3+Ck+usYQNT+LXwDxsOZTNdCVWaTkzRRg9F2yTB5Y/YVEG61kmJpFc2iFu9BJrPnC64llfqB3LZlmL4pg8SyfxwbhWUAU2JrgkPBJ/ijfZsUSKHWAs3dA6+XZbmh4OA89+l5NeKYRWeMhFN+RaZRw4ljIwth25j3Jwnse+6bQGVrWSKom1ZNggyBniQ/MwHqiH80eOaJhegLKYVSyPkoNc4PDoLBNNK0PD3mflnCByA33SWzxKDjc1Mv4Kr5s3UklAHcymHK4Vs3tAviiRsod83kaFlJFxXAlrjGOFExaM42qrhbBknGQkzl0xDtoU1xgHfrzGOBmDKa0xTmxVMZaEg6f9GuG40AhwQTgYOXaFb/CeVkVjwTdwx5FYFnwTTKt4siAcM9anWhCOz2uEA89vjdGMQ19cIxwfwgrh1DKWpuoIx1t/qc3REU4aa3YtCSe0kbkgHCDbRiZw9uAH2wgHy8SUR76JBjRThW8w4QHPjXwDBGtupT9Y161eCCewu7IQjuO860I4GOssh0DCAf3FcqkagalioAOAY0DZQepqkXAquM1GIRz86+2lPkRkcZhGOL7W2io1BCnzgF468xBCLgDLjYRDTmIiqGPphRT8pfZSwjBgKRL4JgiyVRdjJQggGIVwWK8UI7kRDrEFE3khHM8aAUKAmHKbBGyrEI4NeeTvwroUET3ZmAUul8Uu7rmgt/jJgHU6CvzYLxkEvR+p8ab48YUgto+4PTaZ8zH73o+blR9cBMKxjND02QOje70IxJ++eP79IwpApKRX2ysFIGZxVwBiFqviDRReF4BgGFkpAAHvXysAwTML1wUg7FTzQjdtEr7QdkzSVwwqrS7DLExh5U1aWGad4dqEV510Mnd+0YTLGrJPVwAizagUO585XJG+yXH3mvRpd4aI5Wn3teXY88tqyeXanVS/VfPg8/VV16tbZ7NvLMfGE/LXB+Gfuu7E7d/8vfLEO1N5IkgJw7H9D6/Of3rZCTUMU1wbhinuH4aYBv6/GYaPqHaxYxT+vd7F3+tdHFXv4k346LHFLnzkmoap6GcsmGvmPJFraq5dacIsfDULQQND4oJBtgpmDZ18KnkxP8B/Zo2yNl9sHCx+nHYQwok72ppNR+rToo8WT5xOgZV7E4ufnbnAx7qj1CQrBkN/DljiK3mURXrC6lCWMh6Lbqya0FSuuQunaJ7LWM8qhi9OWHCSkC2X9KxnasgHZ6yKhhhZTFTqWZoiyy0llWKJbbP6pMX8kmlcdfmsFHNXyHA7vOhmcCmWcnBFdMyNlhq6LH1tz8pAzy1yLPWxqlRwKOmLE9Z1cFuD9XD3NPe/sOz3WnFgDUg4QQl9M3yR8pcY7rrRrJQWEb3Ys7OBWqrQUGIFnVKsYFbN6DplbrPqQWWe6u113xjn2W/Lb92p+9jTfYkZUpsM0Iirg4iJS2mDId4NSyXuxtqjjiJuqi4sQTqOeWCBcaanFp6bL76yciVrRyZWurXjP21+ob7mXDEx1p4TvZ2uPoEs6ez1l1//+L3+6nFknwQXWUwUDqVxm6W7e2RL8cP9EawfeFgcFFBcemx/YPX8s+2PeQB3uCmS290jm6pX+qSvT5SlWLcU3sTjfa804LtP90cCGQMLUWNI93MAJd4N5LbqLSCjZ6VZw6q5xa7iGN8ZHLmXHkvMoTd2Fu/HcVP1Jo4shYwFaEBcNm4FSDuo7+szu+DBmJoXW85CrtgFnIKeTGFcM6wuLP96Y26s1nd/uUzpsUTWywal5X93fzz/+LPvnv/xhx+/e1eoS82Z+VXDoFeCnnXPwkfG9nW9vKgsL8Wrsd3yVgEzosIPO9nkZHlHT36j2P6zDe4KOX6v9S4V0y2ElHR3n3SaVaf0urd6hZ9loqsgkRKte5MQn3+2MV6Dx8r1oVrnum6Zpfu7RWvW3dLp3uyWAEqN8qnYmDebef1NjJZi8WKL5UDXLbN0f7dozbpbOt2b3ZJb+gKaFrnY3e4W97cwWuaFteqVWbi7U7Re1Sed5pXZB9iNaS+XTuHFE+qeUDOYd2YyrG31dZCrkLrYrKT7UdSaNYyd7jfAkQd9Le9kYZpE57/vGpapDMFL+pfGcpbux1Jr1lh2ut8AyxTktg3jTa2uo+h3DUveOgMnqV0kVNL9WGrNGstO9xtgWf0QElYKoOlSulnIO4YlG26KZ2alwlJJd2PZaVZY9rq3sfQ8NleSZYZO8d1Ee5EL7Zna5C+f/c72Ki26Zjd+tHonV2n/co9Vmr1k3I9u0n0/WCQcquW1jnsUO2az+bNkjUWTJXc0sk6T8UGKUkt2ckuFotxakwOL92Ymfli56isyyS5477g7zk28cfkeKytA+tgud+KVPkGkntd4uljk4i4MR1akpZxZs7xaDXJeMOTb1ZqRG+fFZZYMjoFb5O1iMH504PVFvDUt8cJD9EgVeRgwT/K8voxJKWi8a3JMt+A1lveUMesouGYVJlaVl4RBT+Y9bNzdF3kcUjZMX+U1aIEUIGIeFqq8Oo6XO1VmOlJMlq68Daxd4sRb2JzIwwDLmMYslzVZYCPWJnYZVz5nKVvHqZ2gQz8xxUApk39gbQMnYgkbMsW8B8kzeVIayVxSZyJviDG82wuDTowKvM5Q0hMRBnj9U5Lr9viVJdjEu1s5yjDHz60LmVOMBTK/atgILw/GyPPMES6F1yjyInpvspUsvegAJut6VsixXuDVca1mfMLQTbz2y+MRoCSXrMHxmcPreY0TPCoBUNk6ikw1SyOdtLx5MTfQdPhrIoXxVkD0QhB54IkGZlN7uY+CV0BRXiSF09Ug8spkatGj9lA1XYVMGDjwF89ny+zlys9Nnf4kX4FLtov2sLRvFqLVrWe2U0zeht7aQLc2Lol8BidwFDgmy/dYBi+5syzzoqEPPOaNRrK8q+4q+WTkMHxq37XByYV7We64Uq4QJPtRMu061wmWV6VZZoF2rsZPVbxervSeGQyzxTGIUu/IgRdthhzNwvE9SATPE4RuoPgqKcFxMa541RMo3Mrda/Mo9Bz8zBOM/aDlrVXwYqEuPcgRwmGJd/xCqUmB3+oKYoCQhSIRz2+XPCoVetLxeBmv5TQLkvJghRwQR2pPah4OhcktjzZ0JAgnxsIBf+t7yqTcOLmmuqNY3haPd7WSooqS+bWL02a/oHD1FUwvafTjvIUTP+fQq+cdfiCy4HLfHF5wWHjbrO+bz3RBby7f0GdzmUGNFmS53lXBI7dLygXGPZw8mwaN7VJGBb+Vm95CaOn/c3exUlk01rUbUufu5cdVPJ2z7d2BBw4jGSj37mNDQtNcaM/P3mbBoJZ3jfa+yQT4FOMonlwZ/M4rAtuVxMr1eWGpy0BnMVSY8oznjaCjRhZTmFNuKftqIMrZhcrTOv3Alax+9JVfDHRrSc9pJK+ZGJjKb9EDjTBmIuGH45h9aIQx8Y41cuKjXQuqaKqdBfLtyj3FaszNB3ySVa9IsFJfbQ4+MWald9csbqDoFRSS2U2pZ2OIEeRG4prJm5eowoy04Hq9OaxCQ/f0HEk63XPg0S1RcUq3W4U1baMKghoRFTM7AFWM7QBXMbnrHxXDu/5UMb/rfzVH6PxFzSk6/1JTEO2OasbSea+a4XTermZE3ehQEyg9mNR0Sw89NTvrRqqazXUjW83+OiZQs8WOOdTssmMaNRvtmEnNXjsmm+a6He+pmXHHk2om3fGqmnl3PKxn6pq3b8nHpd6TLzr2ZWrTSkQERloeMOCEoXChjlY/+yC2xanOCuVdRvpPnNyKLH8iKxs4YtbiCOhsxYq5iBTMxNM9lBY4j9Tt5X3OBstk5rgz8x6Y84AKeZ6n1PyZ0nJ5ISYYmKYguHTSqeVNxyRPcq9ubTomzRkEgsDg+nag+xxvI2cClG41wlwGjtq8OpunsJikL8TZQNIybvXToC5QhqtaLSyqvHJ22YTAM56GDKIb7FeM66QKik4+AddpnkDu2qG6pGuz6kBln1tFw81ofPHzGQSOZ8WD46HGNx0EnAT6y5/MXqLEyp0oxUyyaNfjJcJMFQ6hHwJy/tTJkTTl1JRiDgxa66VTu7shwItmEZOcK+dOM8g+GUSjvh1FygFW2w8BuaM7e94Trc2rs3kKi0naDYLu6cmhOsWT+y2aMTlr12i/YmAnVXB08gm8TvMEdNcO1S1dq6cuVPa5VTTcjMb9BkGRvafEi50N53I1YF6SovwggyNg3nA9CAovnjbBt+NcWBvxfN/r6WDAm6m9FG9QT58eehojiVe0t/cKAV7ey+SSdGlPvMhf6eeVvHte6Xn1ZJmXbx91rCWKd5g13xd1Llb95b0adfp/k/eoz/L++VnPhPobHL68kS1+KwUcwKwkkr++kUjOI5uPyEbvH1eaHtA/h4blacvl9YLTokh8bt4Em/bg//grw5vRgedlJ/4hBZeVlZdMGv79x7/9x/Nn33x3fvH8x++fv/rl+c9ffPnDdPryd6f/Aycpg6wKZW5kc3RyZWFtCmVuZG9iagoxMSAwIG9iago3ODM4CmVuZG9iagoxNiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDkwID4+CnN0cmVhbQp4nD2MsQ3AMAgEe6ZggUiAAeN9olT2/m0IcdLwpz/0HoqEh0leZ8MuA0+G5lG4QIOKJjyaMo2lUkOQoyex6SbjUu/e/GfymRS9SQ7yGChenfePtp1w3dp6G/AKZW5kc3RyZWFtCmVuZG9iagoxNyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDg4ID4+CnN0cmVhbQp4nD2NuRHAMAgEc6qgBIF4pH48juT+U5/wEwA77NxcunJjTaxUx0w+hCRm4UUao2iRSmPrDeT4PRQar/3CsKPzdjasrqOhW4Jk2kfIbVe9669bdN7JCxvOCmVuZHN0cmVhbQplbmRvYmoKMTggMCBvYmoKPDwgL0JCb3ggWyAtMTAxNiAtMzUxIDE2NjAgMTA2OCBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzMyCi9TdWJ0eXBlIC9Gb3JtIC9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nE2SS25rMQxD53cV2kAB62+vp0BHefufviPfDgokoGJLJEXnSZMI+feoLVFL+TyaJeotelyUO3O9+P1YnPdk0+tL3EJ0zY33ki7xc6RcQtfA9xPx/t4pfFI3EofzDChLJROJfS6azsStMiTDxDCQZuJIwXXg74ZsBPaLOeK32iXTkfDPTG7lpqyk8PB5amEJq7lbsuxF+lDcw9kyHRH02+yxZzpcvDghI9dz0fLeTGXMcKoNGz7OtYJlWMNcvtjHIy8SEN1T2WlZsKTYTVQJgTBxS07K9+amblMcMpuV5KavrdKavJWtknbIoqV/gxpExt/KG/QgqGRmLAeSvaCCtIaYFx4kgH6roq+JqPJIX3cTVPFUnyd1glGJnj5Y/FxEEe2pHJvFf8gVNq/ZbdsbGQxVLDkaNU+p+VaKu2L9nrXtz4qf5+c/tip78QplbmRzdHJlYW0KZW5kb2JqCjE5IDAgb2JqCjw8IC9CQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDUzMgovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJw9k0tuJjEIhPd9Cl9gJAMG2+eJNKs/99/OV3Qyixa0ebqq/JTX+GMxvp+8d6wceWrYtNdmjK+nvXs48eFRI3cOr1KkfITPkStGrD3Sdlsi8z1Z1MSaNFamauLGcLp9Xo9Jr2exRuwaxyiIsTQ55h2adXtF99X267F92rNgK7bNN32bqpMTv22OVqHaToyzhm3cObGpJvKCLJt9YQsbu7unCQjjhyO7W+brcS6K48sV9Yo32+mtcr8M4KZtz1UELy25X3sUKLeUi18xlUO3yjMc5Ip+dk5btih7T2J3hln91NykiY8DV7oxJjROzqxBdAGj0tc6agRly7h5QcPMHiHLcANyTj8My/bMRcIdFwSseYRCkFzAClwyKSxwtALRgmSy6zSklG9nZ9ptbqYBsoxCL/LEqDJE8VsTKEP3jLyjpCdqK1Wz6ow9tV66quAa3rcqu69QKkV0wrdBv1h2RzXteFC2hRu4t/VsmaBhWN2AIFa0R3p340+KLXhe0vN/HMpme+UCj00XQN2uYWIguxKEKfaIgAMRJOd8dWerpu2cvRtQK5ctzLiTQacCm+GGsD/PmVoM5/eB8kpaPZenGugrz7tBQkJb3z+vK1KYCb04Up80uFCGqFu8skQeirIH2yR6LOandCa73/uyL5OVUVldU9WKoLJK7wsU0F+u1xLx856oo5BUZkvwd/PP8/cfiKjUdQplbmRzdHJlYW0KZW5kb2JqCjIwIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTQ0ID4+CnN0cmVhbQp4nD2POxIDIQxDe06hI+A/nGczqTb3b6MlkAa/sbAlWyg6cvDxGqjseEk7+GmeTjVwN2Nvk8ciU0Gya72QGbiaTkVyow4qOqHliLkU7gkvTrvoJpuTpg9pyCaJJ8rd8lckj1CxYYw9LnVWCu1iRZNpSKexMCKN1RPFmAzA4eJv01ynGX8+9fofe7f3F0y4M9YKZW5kc3RyZWFtCmVuZG9iagoyMSAwIG9iago8PCAvQkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxODEKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicNVA5DgQhDOt5hT+wErnDe0baavb/7YYwU6AYHAc7g0nxIcFvRDaQiRR4gsNxjWSIMYgNqgJaDtMogpc0uge/XGr1EihmiaV6SEspdVzhDJbY5Roy+y6mIF2QDEgNuYaWdKN7qBxObcIJRnmktuYGrrMml882uv/ydkrwiHbjhY/T0HycRmXcXKR1qgh6YkbNyj02eglG3LUcsZy11FKkVIs6UWWw1Q9zNv/u8RrfP+Y3Px4KZW5kc3RyZWFtCmVuZG9iagoyMiAwIG9iago8PCAvQkJveCBbIC0xMDE2IC0zNTEgMTY2MCAxMDY4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNTAKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicPVBJjgMxCLz7FXwgkgswxu9pKafM/69T2E6kboHZamkeU2Z0+WuuKWOkfJov3dlwRjMZM8TT5GmBLm4qgRQLxq6iszojXcCZ4SmAiS+XqIY7hG9LlRcghrnj03QueWmfBET+UiWL6rMYZ6Ou8ct+741dsbhwF39iEwKPFMFaPpQVvkXUWIkyOzKfZjO3dAq+JnyacTKSblisSrwT2XmyUGvJWccY1MeTBBv8rwNY5ziG2KJPi1O6d8q/gDi9cYI6dMfnC0fZ/sVV2z2WMnamQ/e2Ku495EEAq4UIX5cDaEuxgvfNsiYOb9BtCtEehXPhnvb+BxEpYAAKZW5kc3RyZWFtCmVuZG9iagoyMyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDgxID4+CnN0cmVhbQp4nDWMwQ3AMAgD/0zBApUCwaEDVX0l+39rofLAOlnm4NChlzMQk5f6mJitwiNdboGnxgLJDJpOCDSEUbClPBxMvaumPLJehjf96i3vB7J/F7QKZW5kc3RyZWFtCmVuZG9iagoxNCAwIG9iago8PCAvQmFzZUZvbnQgL0RlamFWdVNhbnMtT2JsaXF1ZSAvQ2hhclByb2NzIDE1IDAgUgovRW5jb2RpbmcgPDwgL0RpZmZlcmVuY2VzIFsgNjUgL0EgNzIgL0ggMTAyIC9mIDEyMiAveiBdIC9UeXBlIC9FbmNvZGluZyA+PgovRmlyc3RDaGFyIDAgL0ZvbnRCQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRm9udERlc2NyaXB0b3IgMTMgMCBSCi9Gb250TWF0cml4IFsgMC4wMDEgMCAwIDAuMDAxIDAgMCBdIC9MYXN0Q2hhciAyNTUgL05hbWUgL0RlamFWdVNhbnMtT2JsaXF1ZQovU3VidHlwZSAvVHlwZTMgL1R5cGUgL0ZvbnQgL1dpZHRocyAxMiAwIFIgPj4KZW5kb2JqCjEzIDAgb2JqCjw8IC9Bc2NlbnQgOTI5IC9DYXBIZWlnaHQgMCAvRGVzY2VudCAtMjM2IC9GbGFncyA5NgovRm9udEJCb3ggWyAtMTAxNiAtMzUxIDE2NjAgMTA2OCBdIC9Gb250TmFtZSAvRGVqYVZ1U2Fucy1PYmxpcXVlCi9JdGFsaWNBbmdsZSAwIC9NYXhXaWR0aCAxMzUwIC9TdGVtViAwIC9UeXBlIC9Gb250RGVzY3JpcHRvciAvWEhlaWdodCAwID4+CmVuZG9iagoxMiAwIG9iagpbIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwCjYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgMzE4IDQwMSA0NjAgODM4IDYzNgo5NTAgNzgwIDI3NSAzOTAgMzkwIDUwMCA4MzggMzE4IDM2MSAzMTggMzM3IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYKNjM2IDYzNiAzMzcgMzM3IDgzOCA4MzggODM4IDUzMSAxMDAwIDY4NCA2ODYgNjk4IDc3MCA2MzIgNTc1IDc3NSA3NTIgMjk1CjI5NSA2NTYgNTU3IDg2MyA3NDggNzg3IDYwMyA3ODcgNjk1IDYzNSA2MTEgNzMyIDY4NCA5ODkgNjg1IDYxMSA2ODUgMzkwIDMzNwozOTAgODM4IDUwMCA1MDAgNjEzIDYzNSA1NTAgNjM1IDYxNSAzNTIgNjM1IDYzNCAyNzggMjc4IDU3OSAyNzggOTc0IDYzNCA2MTIKNjM1IDYzNSA0MTEgNTIxIDM5MiA2MzQgNTkyIDgxOCA1OTIgNTkyIDUyNSA2MzYgMzM3IDYzNiA4MzggNjAwIDYzNiA2MDAgMzE4CjM1MiA1MTggMTAwMCA1MDAgNTAwIDUwMCAxMzUwIDYzNSA0MDAgMTA3MCA2MDAgNjg1IDYwMCA2MDAgMzE4IDMxOCA1MTggNTE4CjU5MCA1MDAgMTAwMCA1MDAgMTAwMCA1MjEgNDAwIDEwMjggNjAwIDUyNSA2MTEgMzE4IDQwMSA2MzYgNjM2IDYzNiA2MzYgMzM3CjUwMCA1MDAgMTAwMCA0NzEgNjE3IDgzOCAzNjEgMTAwMCA1MDAgNTAwIDgzOCA0MDEgNDAxIDUwMCA2MzYgNjM2IDMxOCA1MDAKNDAxIDQ3MSA2MTcgOTY5IDk2OSA5NjkgNTMxIDY4NCA2ODQgNjg0IDY4NCA2ODQgNjg0IDk3NCA2OTggNjMyIDYzMiA2MzIgNjMyCjI5NSAyOTUgMjk1IDI5NSA3NzUgNzQ4IDc4NyA3ODcgNzg3IDc4NyA3ODcgODM4IDc4NyA3MzIgNzMyIDczMiA3MzIgNjExIDYwOAo2MzAgNjEzIDYxMyA2MTMgNjEzIDYxMyA2MTMgOTk1IDU1MCA2MTUgNjE1IDYxNSA2MTUgMjc4IDI3OCAyNzggMjc4IDYxMiA2MzQKNjEyIDYxMiA2MTIgNjEyIDYxMiA4MzggNjEyIDYzNCA2MzQgNjM0IDYzNCA1OTIgNjM1IDU5MiBdCmVuZG9iagoxNSAwIG9iago8PCAvQSAxNiAwIFIgL0ggMTcgMCBSIC9mIDIwIDAgUiAveiAyMyAwIFIgPj4KZW5kb2JqCjI4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjU5ID4+CnN0cmVhbQp4nD1SSXLDMAy7+xV8AndJ70mnJ+f/1wL01JcQY4oACKZ3i8rZ+GkrWX7kxy47SyK3fAdtk/uKqgekboLMJcclV4hZyudKkFi0lJlYn6kOys81qFX4wk/MTEyHJBFLyEk9irB+Xgf3oH69pPNbZPyjY4PSW5JMBZ0a7pWjlNiwVJ8a5B403ZRWn5l2ZQcsjTdkpSZ1+vXT4wdLMKUvEtFBiMSf5HKHLAspB/F2rt5AeFe7INVTKw87RJqPkd5SBas5MwFLRtMOI2Bt1pggVQK8RWsItBbi8oVOKyI+OTd0ME1VnoXIsFLhWHvPaA0Xuoa80nB6knH/+R+8K97X7x/a82ZkCmVuZHN0cmVhbQplbmRvYmoKMjkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMzIgPj4Kc3RyZWFtCnicNVE7cgUxCOt9Cl0gM+Zvn2czr0ru30awk2ZhAQkJ5z3YiMSXGNId5YpvWZ1mGX4ni7z4WSmcvBdRgVRFWCHt4FnOaobBcyNT4HImPsvMJ9NixwKqiTjOjpxmMAgxjetoOR1mmgc9IdcHI27sNMtVDGm9W6rX91r+U0X5yLqb5dYpm1qpW/SMPYnLzuupLe0Lo47ipiDS4WOH9yBfxJzFRSfSzX4z5bCSNASnBfAjMZTq2eE1wsTPjARP2dPpfZSG1z5our53L+jIzYRM5RbKSMWTlcaYMVS/Ec0k9f0/0LM+f5owVEcKZW5kc3RyZWFtCmVuZG9iagozMCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDc3ID4+CnN0cmVhbQp4nDM3NVIwULC0ABJmpiYK5kaWCimGXEA+iJXLZWhpDmblgFkmxgZAlqmpKRILIgvTC2HB5GC0sYk51AQECyQHtjYHZlsOVxoAnuAbmgplbmRzdHJlYW0KZW5kb2JqCjMxIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjEyID4+CnN0cmVhbQp4nDVQOQ4DMQjs/Yr5QCSDbTDv2Shd/t+GAaVYMVrmwn4dE8fwkgVfAt+Kt4wVG2aK71iqhdQObB2oLpyreIZcwdELsYmdFpzLNjeJ1BVkSERpZFtu6BKKNkWn5O9Nc0s35fakSdNtWhmYehlydgQRQ8lgCWq6Fk1YtD0V/1OeOor3fccOK3Tc4dOTH/U9w2c+h0u9xfao2YlEui/IkNOaSwlNNNnRr8gUzjw2pJDOIEFSXIJrZZDt6ZejAxIwMbcsQHZXopwlacfS/zOe8fkBAdtTqQplbmRzdHJlYW0KZW5kb2JqCjMyIDAgb2JqCjw8IC9CQm94IFsgLTEwMjEgLTQ2MyAxNzk0IDEyMzMgXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIzNwovU3VidHlwZSAvRm9ybSAvVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJw9UbtxxTAM6z0FRuBH/Gied5cq2b8NKDkpeIApEQTkpyzRhZ9niOD7We7/yAOSrVBthCc0FZEN08DnSRFYbqQm3F7c54RslSP24lwgwhDtPAlppAsWOxkL3hc/j6seZqy5Yfy+M5p9VHTVUR28ew7jZk0/TpTd682sjlub+3TvrhOHa0gmn/cfnJRKp5csgzpLuLA2mhrW47woxljMOP4nqrBNsrajCsHSJUgq0IAYShLGgMUt/iInWg4L2psbaeudyU6qNIqGF6MM3qD1RjiKdJF8mGsrg7GpmDa++eQlN+j7Z7+fr18Da1rrCmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMjcgPj4Kc3RyZWFtCnicRZBLjgMhEEP3nMJHoP5wno6y6tx/Oy460WywJSjXM7kDE3vxyEyUbrxkuDvMFZ/hGTBz+EqYbMRM6E5cI5SuFOFUnwiOy9686aCJe0TOo54FWdXODWoBZ5Lmgu2CLueMFTfOya1G5c30o9cQvml3H9d5h/ZI497DVL7OOdXOu4oIaQtZ1bS+kGwUyQ5rPypN287LELHgbBpW6BzeCLtXdydLGH6/8jAlEz8P3fpRfF03o+sUZydXJmvPeehJ6V/1yqMPxXEp6Bex7cwk91+nU5KpU3tn72n9p7jH+w+QblY5CmVuZHN0cmVhbQplbmRvYmoKMzQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMDQgPj4Kc3RyZWFtCnicPZI7ksMwDEN7nYIXyIz4k+TzZCeV9/7tPjLJVoBJiQAoL3WZsqY8IGkmCf/R4eFiO+V32J7NzMC1RC8TyynPoSvE3EX5spmNurI6xarDMJ1b9Kici4ZNk5rnKksZtwuew7WJ55Z9xA83NKgHdY1Lwg3d1WhZCs1wdf87vUfZdzU8F5tU6tQXjxdRFeb5IU+ih+lK4nw8KCFcezBGFhLkU9FAjrNcrfJeQvYOtxqywkFqSeezJzzYdXpPLm4XzRAPZLlU+E5R7O3QM77sSgk9ErbhWO59O5qx6RqbOOx+70bWyoyuaCF+yFcn6yVg3FMmRRJkTrZYbovVnu6hKKZzhnMZIOrZioZS5mJXq38MO28sL9ksyJTMCzJGp02eOHjIfo2a9HmV53j9AWzzczsKZW5kc3RyZWFtCmVuZG9iagozNSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDU0ID4+CnN0cmVhbQp4nDM2NlcwUDA0MlfQNTI2VTAyNFAwNzNRSDHkgjFzwSywbA4XXCGECZLPgavM4UoDAEyQDxUKZW5kc3RyZWFtCmVuZG9iagozNiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI3OSA+PgpzdHJlYW0KeJw9UjuSxSAM63MKX4AZ8BfOk52tsvdvV4K8V2SsREaSHdJSugwNaSNVYgyp7PIzLsK2VP4OIvtcPr/Q1jrQnIeji40JoCn3pasDdhWtkha+6ygyBOYQ2GiaaE5RcAoJtX3acJCH+gDrMiJ2vS8GJXo2sq1D9iD2E6kZUkE58I6EUISHzb5j+DhxPO3NE2BOngw4I3v1M04pXTlhORQwMrfDLbDe12dfz0a5iLzmB2EOIscicmJTEwySQLEcXo508NRTozYD5FFcMFHHbLHAz71nPugxpFPoke3YXC6kXmTwhfnZofBgP7cABiqqtZ0GO1i9v45jvYYNv4/hWuSO24otHKBNFw7EO8ERWe/vLXmu338Hcm4GCmVuZHN0cmVhbQplbmRvYmoKMzcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNzYgPj4Kc3RyZWFtCnicPVJLjugwCNvnFFwgUvgmPU9Hs+q7//bZtJoVFmBjSMpLlqilTC2TVJVdS350dO4y+Tc0r0bPsPXmzEPmSbE4MrfKPQzkmVus0Gtv1KsLALFI7tQS2yXGlkvFkmSHrO0Qd2TQ4cUq2cz42sION2uOR1IXKl6nBwX5jDDwTsx9vollITRXGW23wEEPFqgDPTALE7ki491rEz2NeAugrA+Zv4guN9Rcj2xMgFO42gveqZTWMQ8ViaIc7EYavZ+j5jihw9s9Yjn2cglHBt7iaMd78EWInkZWRKx+yLMR+YYNqUiPmMob6m4fevyNrdhof3YmScHXX9bbTDXSueDUXK3WX4NHaPDeqOHz90ue8fsfISZuEgplbmRzdHJlYW0KZW5kb2JqCjM4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjMwID4+CnN0cmVhbQp4nDVRSW7DMAy86xXzgQDiLr/HQU/t/68d0glgYGhLnM0RGxsReInBz0HkxlvWjJr4m8ld8bs8FR4Jt4InUQRehnvZCS5vGJf9OMx88F5aOZMaTzIgF9n08ETIYJdA6MDsGtRhm2kn+oaEz45INRtZTl9L0EurEChP2X6nC0q0rerP7bMutO1rTzjZ7aknlU8gnluyApeNV0wWYxn0ROUuxfRBqrOFnoTyonwOsvmoIRJdopyBJwYHo0A7sOe2n4lXhaB1dZ+2jaEaKR1P/zY0NUki5BMlnNnSuFv4/p57/fwDplRTnwplbmRzdHJlYW0KZW5kb2JqCjM5IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNjggPj4Kc3RyZWFtCnicMzY2VzBQMDQEkUZGBgqmQFaKIRdIwNDIRCGXCyQIYuWAWQZAGqI4B64GwgJphKgGsSCqjS2NobIIFkQ2DQBHohbLCmVuZHN0cmVhbQplbmRvYmoKNDAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA2NiA+PgpzdHJlYW0KeJwzNrRQMFAwN1fQNTQ0VTAyMlAwNDJRSDHkMjQ0BzNzuWCCOWCWiQGQYQgkwRpyuGBac8A6ILJQrTlcaQBNOBH1CmVuZHN0cmVhbQplbmRvYmoKNDEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMjcgPj4Kc3RyZWFtCnicNU87sgMhDOs5hS6QGYxtYM+zmVQv92+fZLINEv5I8vRERyZe5sgIrNnxthYZiBn4FlPxrz3tw4TqPbiHCOXiQphhJJw167ibp+PFv13lM9bBuw2+YpYXBLYwk/WVxZnLdsFYGidxTrIbY9dEbGNd6+kU1hFMKAMhne0wJcgcFSl9sqOMOTpO5InnYqrFLr/vYX3BpjGiwhxXBU/QZFCWPe8moB0X9N/Vjd9JNIteAjKRYGGdJObOWU741WtHx1GLIjEnpBnkMhHSnK5iCqEJxTo7CioVBZfqc8rdPv9oXVtNCmVuZHN0cmVhbQplbmRvYmoKNDIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNDUgPj4Kc3RyZWFtCnicRVC7jUMxDOs9BRcIYP0se553SJXbvz1KRnCFIVo/kloSmIjASwyxlG/iR0ZBPQu/F4XiM8TPF4VBzoSkQJz1GRCZeIbaRm7odnDOvMMzjDkCF8VacKbTmfZc2OScBycQzm2U8YxCuklUFXFUn3FM8aqyz43XgaW1bLPTkewhjYRLSSUml35TKv+0KVsq6NpFE7BI5IGTTTThLD9DkmLMoJRR9zC1jvRxspFHddDJ2Zw5LZnZ7qftTHwPWCaZUeUpnecyPiep81xOfe6zHdHkoqVV+5z93pGW8iK126HV6VclUZmN1aeQuDz/jJ/x/gOOoFk+CmVuZHN0cmVhbQplbmRvYmoKNDMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzOTIgPj4Kc3RyZWFtCnicPVJLbgUxCNvPKbhApfBNcp6p3u7df1ubzFSqCi8DtjGUlwypJT/qkogzTH71cl3iUfK9bGpn5iHuLjam+FhyX7qG2HLRmmKxTxzJL8i0VFihVt2jQ/GFKBMPAC3ggQXhvhz/8ReowdewhXLDe2QCYErUbkDGQ9EZSFlBEWH7kRXopFCvbOHvKCBX1KyFoXRiiA2WACm+qw2JmKjZoIeElZKqHdLxjKTwW8FdiWFQW1vbBHhm0BDZ3pGNETPt0RlxWRFrPz3po1EytVEZD01nfPHdMlLz0RXopNLI3cpDZ89CJ2Ak5kmY53Aj4Z7bQQsx9HGvlk9s95gpVpHwBTvKAQO9/d6Sjc974CyMXNvsTCfw0WmnHBOtvh5i/YM/bEubXMcrh0UUqLwoCH7XQRNxfFjF92SjRHe0AdYjE9VoJRAMEsLO7TDyeMZ52d4VtOb0RGijRB7UjhE9KLLF5ZwVsKf8rM2xHJ4PJntvtI+UzMyohBXUdnqots9jHdR3nvv6/AEuAKEZCmVuZHN0cmVhbQplbmRvYmoKNDQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA3MSA+PgpzdHJlYW0KeJyzMLZQMFAwNDBTMDQ3UjA3NlIwMTVRSDHkAgmBmLlcMMEcMMsYqCwHLItgQWRBLCNTU6gOEAuiwxCuDsGCyKYBAOvnGDIKZW5kc3RyZWFtCmVuZG9iago0NSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMyA+PgpzdHJlYW0KeJxNj0ESwzAIA+9+hZ6AsQHznnR6Sv5/LZA27gXtjICRhjAIPGIM6zAlvHr74VWkS3A2jvklGUU8CGoL3BdUBUdjip342N2h7KXi6RRNi+sRc9O0pHQ3USptvZ3I+MB9n94fVbYknYIeW+qELtEk8kUCc9hUMM/qxktLj6ft2d4fZj4z1wplbmRzdHJlYW0KZW5kb2JqCjQ2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjQ3ID4+CnN0cmVhbQp4nE1Ru21EMQzr3xRc4ADra3meC1Jd9m9DyQiQwiChLymnJRb2xksM4QdbD77kkVVDfx4/MewzLD3J5NQ/5rnJVBS+FaqbmFAXYuH9aAS8FnQvIivKB9+PZQxzzvfgoxCXYCY0YKxvSSYX1bwzZMKJoY7DQZtUGHdNFCyuFc0zyO1WN7I6syBseCUT4sYARATZF5DNYKOMsZWQxXIeqAqSBVpg1+kbUYuCK5TWCXSi1sS6zOCr5/Z2N0Mv8uCounh9DOtLsMLopXssfK5CH8z0TDt3SSO98KYTEWYPBVKZnZGVOj1ifbdA/59lK/j7yc/z/QsVKFwqCmVuZHN0cmVhbQplbmRvYmoKNDcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA5MCA+PgpzdHJlYW0KeJxNjUESwCAIA++8Ik9QRND/dHrS/1+r1A69wE4CiRZFgvQ1aksw7rgyFWtQKZiUl8BVMFwL2u6iyv4ySUydhtN7twODsvFxg9JJ+/ZxegCr/XoG3Q/SHCJYCmVuZHN0cmVhbQplbmRvYmoKNDggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMzggPj4Kc3RyZWFtCnicRVJLcsUwCNvnFFwgM+Zn4/O8Tlfp/beVcDrdPPQMCAkyPWVIptw2lmSE5BzypVdkiNWQn0aORMQQ3ymhwK7yubyWxFzIbolK8aEdP5elNzLNrtCqt0enNotGNSsj5yBDhHpW6MzuUdtkw+t2Iek6UxaHcCz/QwWylHXKKZQEbUHf2CPobxY8EdwGs+Zys7lMbvW/7lsLntc6W7FtB0AJlnPeYAYAxMMJ2gDE3NreFikoH1W6iknCrfJcJztQttCqdLw3gBkHGDlgw5KtDtdobwDDPg/0okbF9hWgqCwg/s7ZZsHeMclIsCfmBk49cTrFkXBJOMYCQIqt4hS68R3Y4i8Xroia8Al1OmVNvMKe2uLHQpMI71JxAvAiG25dHUW1bE/nCbQ/KpIzYqQexNEJkdSSzhEUlwb10Br7uIkZr43E5p6+3T/COZ/r+xcWuIPgCmVuZHN0cmVhbQplbmRvYmoKNDkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNjMgPj4Kc3RyZWFtCnicRZC5dQQxDENzVYESeIA66hk/R7P9pwtpvN5A+niEeIg9CcNyXcWF0Q0/3rbMNLyOMtyN9WXG+KixQE7QBxgiE1ejSfXtijNU6eHVYq6jolwvOiISzJLjq0AjfDqyx0Nb25l+Oq9/7CHvE/8qKuduYQEuqu5A+VIf8dSP2VHqmqGPKitrHmravwi7IpS2fVxOZZy6ewe0wmcrV/t9A6jnOoAKZW5kc3RyZWFtCmVuZG9iago1MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDUyID4+CnN0cmVhbQp4nDM2M1QwUDCxVDAyNlEwNjQCYhOFFEMuoAiIlcsFE8sBs0CqcrigynNgqnK40gDpCQ3ACmVuZHN0cmVhbQplbmRvYmoKNTEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA2OCA+PgpzdHJlYW0KeJwzMrdQMFCwNAEShhYmCuZmBgophlxAvqmJuUIuF0gMxMoBswyAtCWcgohbQjRBlIJYEKVmJmYQSTgDIpcGAMm0FeUKZW5kc3RyZWFtCmVuZG9iago1MiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDgxID4+CnN0cmVhbQp4nD3MuxWAMAgF0D5TvBFCfIDs47HS/VvBRBu4fNUDHSEZ1A1uHYe0rEt3k33qerWJpMiA0lNqXBpOjKhpfal9auC7G+ZL1Yk/zc/nA4fHGWsKZW5kc3RyZWFtCmVuZG9iago1MyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDQ1ID4+CnN0cmVhbQp4nDMyt1AwULA0ARKGFiYK5mYGCimGXJYQVi4XTCwHzALRlnAKIp4GAJ99DLUKZW5kc3RyZWFtCmVuZG9iago1NCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI1NSA+PgpzdHJlYW0KeJxFkUuSAyAIRPeegiOA/OQ8mZpVcv/tNJhMNnaXqP2ESiOmEiznFHkw/cjyzWS26bUcq52NAooiFMzkKvRYgdWdKeLMtUS19bEyctzpHYPiDeeunFSyuFHGOqo6FTim58r6qu78uCzKviOHMgVs1jkONnDltmGME6PNVneH+0SQp5Opo+J2kGz4g5PGvsrVFbhONvvqJRgHgn6hCUzyTaB1hkDj5il6cgn28XG780Cwt7wJpGwI5MgQjA5Bu06uf3Hr/N7/OsOd59oMV4538TtMa7vjLzHJirmARe4U1PM9F63rDB3vyZljctN9Q+dcsMvdQabP/B/r9w9QimaICmVuZHN0cmVhbQplbmRvYmoKNTUgMCBvYmoKPDwgL0JCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzcKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnic4zI0MFMwNjVVyOUyNzYCs3LALCNzIyALJItgQWTTAAFfCgoKZW5kc3RyZWFtCmVuZG9iago1NiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE2MSA+PgpzdHJlYW0KeJxFkEsSwyAMQ/ecQkfwRwZ8nnS6Su+/rSFNs4CnsUAGdycEqbUFE9EFL21Lugs+WwnOxnjoNm41EuQEdYBWpONolFJ9ucVplXTxaDZzKwutEx1mDnqUoxmgEDoV3u2i5HKm7s75R3D1X/VHse6czcTAZOUOhGb1Ke58mx1RXd1kf9JjbtZrfxX2qrC0rKXlhNvOXTOgBO6pHO39BalzOoQKZW5kc3RyZWFtCmVuZG9iago1NyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMyMCA+PgpzdHJlYW0KeJw1UbtxxTAM6zUFF/Cd+JU0j3Ovytu/DUA7FWEaBECqvGRKuVzqklWywuRHh+oUTfk+YKb8DvWQ4+ge2SG6U9aWexgIy8Q8pY5YTZZ7uAWBLwxNibmF8/cI6CsGozATgbrF3z9AsyQwaXDwU5BrrVpiiQ48LBZYsyvMrRopVMhVfDs2uQcFcnGz0KccmhS33ILwZYhkR2qxr8tlKfK79QkYhBXmiE8UiYXngQ5mIvEnA2J79tliV1cvqhEZ1kmHB1IE0mxuEjA0RbLqgxvYV8c1P09H2cHJQb+Kwfg2OJkvSXlfBaEQjxf+Ds/ZyLGSQyQU8n21wIgjbIARoU/tIxBlIDRF9+6ZUj4mVYrvAEYhHH2qVzK8F5HZaobN/xld2SoKBlVZH59GcCaDSTjzZKMK01K107/73OPzB2NjeoAKZW5kc3RyZWFtCmVuZG9iago1OCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIxNCA+PgpzdHJlYW0KeJw9ULsRQzEI6z0FC+TOfO03z8uly/5tJJykQjZCEpSaTMmUhzrKkqwpTx0+S2KHvIflbmQ2JSpFL5OwJffQCvF9ieYU993VlrNDNJdoOX4LMyqqGx3TSzaacCoTuqDcwzP6DW10A1aHHrFbINCkYNe2IHLHDxgMwZkTiyIMSk0G/61y91Lc7z0cb6KIlHTwrvnl9MvPLbxOPY5Eur35imtxpjoKRHBGavKKdGHFsshDpNUENT0Da7UArt56+TdoR3QZgOwTieM0pRxD/9a4x+sDh4pS9AplbmRzdHJlYW0KZW5kb2JqCjU5IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggODAgPj4Kc3RyZWFtCnicRYy7DcAwCER7pmAEfiZmnyiVs38bIErccE+6e7g6EjJT3mGGhwSeDCyGU/EGmaNgNbhGUo2d7KOwbl91geZ6U6v19wcqT3Z2cT3Nyxn0CmVuZHN0cmVhbQplbmRvYmoKNjAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMzYgPj4Kc3RyZWFtCnicTVBLbkQhDNtzilzgSSQhAc5D1VXn/tuxw1TtKoYYf0gP6bJVHutTYnWJ7PKlTZfKMnkVqOVP2/9RDAJu/9DIQbS3jJ1i5hLWxcIkPOU0Ixsn1ywfjztPG2aFxsSN450uGWCfFgE1W5XNgTltOjdAupAat6qz3mRQDCLqQs0Hky6cp9GXiDmeqGBKdya1kBtcPtWhA3FavQq5Y4uTb8QcWaHAYdBMcdZfAdaoybJZyCBJhiHOfaN7lAqNqMp5KxXCD5OhEfWG1aAGlbmFoqnlkvwd2gIwBbaMdekMSoGqAMHfKqd9vwEkjV1TCmVuZHN0cmVhbQplbmRvYmoKNjEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNDcgPj4Kc3RyZWFtCnicPU+5DQMxDOs9BRc4wHosW/NckOqyfxvKRlIIIkDxkWVHxwpcYgKTjjkSL2k/+GkagVgGNUf0hIphWOBukgIPgyxKV54tXgyR2kJdSPjWEN6tTGSiPK8RO3AnF6MHPlQbWR56QDtEFVmuScNY1VZdap2wAhyyzsJ1PcyqBOXRJ2spH1BUQr10/5972vsLAG8v6wplbmRzdHJlYW0KZW5kb2JqCjYyIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTQ5ID4+CnN0cmVhbQp4nDWPSw4DIQxD9zmFLzBSfoRwHqqupvffNmFaCQkL2y/BFoORjEtMYOyYY+ElVE+tPiQjj7pJORCpUDcET2hMDDNs0iXwynTfMp5bvJxW6oJOSOTprDYaooxmXsPRU84Km/7L3CRqZUaZAzLrVLcTsrJgBeYFtTz3M+6oXOiEh53KsOhOMaLcZkYafv/b9P4CezIwYwplbmRzdHJlYW0KZW5kb2JqCjYzIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNDkgPj4Kc3RyZWFtCnicMza0UDBQMDQwB5JGhkCWkYlCiiEXSADEzOWCCeaAWQZAGqI4B64mhysNAMboDSYKZW5kc3RyZWFtCmVuZG9iago2NCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE1NyA+PgpzdHJlYW0KeJxFkLkRQzEIRHNVQQkSsAjqscfRd/+pF/lKtG8ALYevJVOqHyciptzXaPQweQ6fTSVWLNgmtpMachsWQUoxmHhOMaujt6GZh9TruKiquHVmldNpy8rFf/NoVzOTPcI16ifwTej4nzy0qehboK8LlH1AtTidSVAxfa9igaOcdn8inBjgPhlHmSkjcWJuCuz3GQBmvle4xuMF3QE3eQplbmRzdHJlYW0KZW5kb2JqCjY1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzMyID4+CnN0cmVhbQp4nC1SOY4kMQzL/Qp+YADr8vGeHkzU+/90SVUFBapsyzzkcsNEJX4skNtRa+LXRmagwvCvq8yF70jbyDqIa8hFXMmWwmdELOQxxDzEgu/b+Bke+azMybMHxi/Z9xlW7KkJy0LGizO0wyqOwyrIsWDrIqp7eFOkw6kk2OOL/z7FcxeCFr4jaMAv+eerI3i+pEXaPWbbtFsPlmlHlRSWg+1pzsvkS+ssV8fj+SDZ3hU7QmpXgKIwd8Z5Lo4ybWVEa2Fng6TGxfbm2I+lBF3oxmWkOAL5mSrCA0qazGyiIP7I6SGnMhCmrulKJ7dRFXfqyVyzubydSTJb90WKzRTO68KZ9XeYMqvNO3mWE6VORfgZe7YEDZ3j6tlrmYVGtznBKyV8NnZ6cvK9mlkPyalISBXTugpOo8gUS9iW+JqKmtLUy/Dfl/cZf/8BM+J8AQplbmRzdHJlYW0KZW5kb2JqCjY2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNjggPj4Kc3RyZWFtCnicMzM2UzBQsDACEqamhgrmRpYKKYZcQD6IlcsFE8sBs8wszIEsIwuQlhwuQwtjMG1ibKRgZmIGZFkgMSC60gBy+BKRCmVuZHN0cmVhbQplbmRvYmoKNjcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMTcgPj4Kc3RyZWFtCnicNVJLckMxCNu/U3CBzpi/fZ50smruv62EJyuwLUBCLi9Z0kt+1CXbpcPkVx/3JbFCPo/tmsxSxfcWsxTPLa9HzxG3LQoEURM9+DInFSLUz9ToOnhhlz4DrxBOKRZ4B5MABq/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      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm = 1000  # Hz\n",
    "QBS = 2 / 3\n",
    "B, A, b, a = audiofilter.biquad_bs2nd(fm, QBS, fs)\n",
    "bode_plot(B, A, b, a)\n",
    "print(\"fcut_low =\", fcl, \"Hz\")\n",
    "print(\"fmid =\", fm, \"Hz\")\n",
    "print(\"fcut_high =\", fch, \"Hz\")\n",
    "print(\"QBS =\", QBS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"allpass1st\"></a>\n",
    "### 1st Order Allpass `ap1st`\n",
    "\n",
    "\\cite{TietzeSchenk2008}\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| 0 | $\\frac{-\\text{a}_\\text{i}}{\\omega_c}$ | 1 | 0 | $\\frac{+\\text{a}_\\text{i}}{\\omega_c}$ | 1 | \n",
    "\n",
    "with cut frequency $\\omega_c=2 \\pi f_c$ in rad/s and filter characteristic coefficient $\\text{a}_\\text{i}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [ 0.0000000000000000e+00 -1.5915494309189535e-04  1.0000000000000000e+00]\n",
      "A = [0.0000000000000000e+00 1.5915494309189535e-04 1.0000000000000000e+00]\n",
      "b = [-0.8769764629927569   0.12302353700724311  1.                 ]\n",
      "a = [ 1.                   0.12302353700724311 -0.8769764629927569 ]\n"
     ]
    },
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   "source": [
    "fc = 1000  # Hz\n",
    "B, A, b, a = audiofilter.biquad_ap1st(fc, fs)\n",
    "bode_plot(B, A, b, a)"
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   "source": [
    "<a id=\"allpass2nd\"></a>\n",
    "### 2nd Order Allpass `ap2nd`\n",
    "\n",
    "\\cite{TietzeSchenk2008}\n",
    "\n",
    "| $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| $\\frac{\\text{b}_\\text{i}}{\\omega_c^2}$ | $\\frac{-\\text{a}_\\text{i}}{\\omega_c}$ | 1 | $\\frac{\\text{b}_\\text{i}}{\\omega_c^2}$ | $\\frac{+\\text{a}_\\text{i}}{\\omega_c}$ | 1 |\n",
    "\n",
    "with cut frequency $\\omega_c=2 \\pi f_c$ in rad/s and filter characteristic coefficients $\\text{b}_\\text{i}$ and $\\text{a}_\\text{i}$"
   ]
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  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [ 2.5330295910584447e-08 -2.2507907903927655e-04  1.0000000000000000e+00]\n",
      "A = [2.5330295910584447e-08 2.2507907903927655e-04 1.0000000000000000e+00]\n",
      "b = [ 0.8310055893467575 -1.815341082704568   1.                ]\n",
      "a = [ 1.                 -1.815341082704568   0.8310055893467575]\n"
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   "source": [
    "fc = 1000  # Hz\n",
    "B, A, b, a = audiofilter.biquad_ap2nd(fc, fs)\n",
    "bode_plot(B, A, b, a)"
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   "source": [
    "<a id=\"peq2nd\"></a>\n",
    "### 2nd Order PEQ `peq2nd`\n",
    "\n",
    "cf. \\cite{Bristow-Johnson1994}, \\cite{Christensen2003}, \\cite{Zoelzer2008}, \\cite{Zoelzer2011}\n",
    "\n",
    "| | $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| $G\\leq0$ | $\\frac{1}{\\omega_\\text{m}^2}$ | $\\frac{\\gamma}{Q_\\text{BP}\\,\\omega_\\text{m}}$ | 1 | $\\frac{1}{\\omega_\\text{m}^2}$ | $\\frac{\\gamma/g}{Q_\\text{BP}\\,\\omega_\\text{m}}$ | 1 |\n",
    "$G>0$ | $\\frac{1}{\\omega_\\text{m}^2}$ | $\\frac{\\delta}{Q_\\text{BP}\\,\\omega_\\text{m}}$ | 1 | $\\frac{1}{\\omega_\\text{m}^2}$ | $\\frac{\\delta/g}{Q_\\text{BP}\\,\\omega_\\text{m}}$ | 1 |       \n",
    "\n",
    "with  $g=10^{\\frac{G}{20}}$, mid frequency $\\omega_m=2 \\pi f_m$ in rad/s, quality $Q_\\text{BP}$ and gain $G$ in dB\n",
    "        \n",
    "* **type I:** \n",
    "$\\gamma=g\\,,\\delta=g$ \n",
    "\n",
    "for $G\\gg 0$ bandwidth is similar to that of the 2nd order bandpass\n",
    "\n",
    "for $G\\ll 0$ bandwidth is similar to that of the 2nd order bandstop\n",
    "\n",
    "* **type II:**\n",
    "$\\gamma=1\\,,\\delta=g$\n",
    "\n",
    "for $G\\gg 0$ bandwidth is similar to that of the 2nd order bandpass\n",
    "\n",
    "for $G<0$ the transfer function is inverted from $G>0$\n",
    "\n",
    "* **default: type III (one-half pad loss):**\n",
    "$\\gamma=g^{1/2}\\,,\\delta=g^{1/2}$\n",
    "\n",
    "cut frequencies are located at $G/2$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [2.5330295910584447e-08 4.7633379028841317e-04 1.0000000000000000e+00]\n",
      "A = [2.5330295910584447e-08 1.1964963846949948e-04 1.0000000000000000e+00]\n",
      "b = [ 1.1397065711701546 -1.889962496723752   0.7665643374357936]\n",
      "a = [ 1.                 -1.889962496723752   0.9062709086059483]\n"
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      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BW = 2  # bandwidth in octaves\n",
    "fm = 1000  # Hz\n",
    "G = 12  # dB\n",
    "Q = audiofilter.q_from_bw(BW)\n",
    "B, A, b, a = audiofilter.biquad_peq2nd(fm, G, Q, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"lowshv1st\"></a>\n",
    "### 1st Order Low-Shelving `lshv1st`\n",
    "\n",
    "cf. \\cite{Christensen2003}, \\cite{Zoelzer2008}, \\cite{Zoelzer2011}\n",
    "\n",
    "| | $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| $G\\leq0$ | 0 | $\\frac{1}{\\omega_\\text{c}}$ | $\\alpha^{+2}$ | 0 | $\\frac{1}{\\omega_\\text{c}}$ | $g^{-1}\\, \\alpha^{+2}$ | \n",
    "| $G>0$ | 0 | $\\frac{1}{\\omega_\\text{c}}$ | $g^{+1}\\, \\alpha^{-2}$ | 0 | $\\frac{1}{\\omega_\\text{c}}$ | $\\alpha^{-2}$ |\n",
    "\n",
    "with $g=10^{\\frac{G}{20}}$, cut frequency $\\omega_c=2 \\pi f_c$ in rad/s and gain $G$ in dB\n",
    "\n",
    "* **type I:**\n",
    "$\\alpha=1$ \n",
    "\n",
    "for $G\\gg 0$ cut frequency is at $G$-3 dB\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at $G$+3 dB\n",
    "\n",
    "* **type II:**\n",
    "$\\alpha=g^{+1/2}$\n",
    "\n",
    "for $G\\gg 0$ cut frequency is at +3 dB\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at -3 dB\n",
    "\t\t\n",
    "* **default: type III (one-half pad loss):**\n",
    "$\\alpha=g^{+1/4}$\n",
    "\n",
    "cut frequency is located at $G/2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [0.0000000000000000e+00 1.5915494309189535e-04 1.9952623149688793e+00]\n",
      "A = [0.0000000000000000e+00 1.5915494309189535e-04 5.0118723362727224e-01]\n",
      "b = [ 1.0948123130222311  0.2532341748159276 -0.8415781382063036]\n",
      "a = [ 1.                   0.06360954877146535 -0.9363904512285347 ]\n"
     ]
    },
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       "   <rect height=\"157.5\" width=\"253.636364\" x=\"50.595312\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pe01f8e596d\">\n",
       "   <rect height=\"157.5\" width=\"253.636364\" x=\"50.595312\" y=\"211.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pc89701eecd\">\n",
       "   <rect height=\"253.636364\" width=\"253.636364\" x=\"354.958949\" y=\"68.749943\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fc = 1000  # Hz\n",
    "G = 12  # dB\n",
    "B, A, b, a = audiofilter.biquad_lshv1st(fc, G, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"lowshv2nd\"></a>\n",
    "### 2nd Order Low-Shelving `lshv2nd`\n",
    "\n",
    "cf. \\cite{Bristow-Johnson1994}, \\cite{Christensen2003}, \\cite{Zoelzer2008}, \\cite{Zoelzer2011}\n",
    "\n",
    "| | $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| $G\\leq0$ | $\\frac{1}{\\omega_\\text{c}^2}$ | $\\frac{\\alpha^{+1}}{Q_\\text{z}\\,\\omega_\\text{c}}$ | $\\alpha^{+2}$ | $\\frac{1}{\\omega_\\text{c}^2}$ |  $\\frac{g^{-1/2}\\,\\alpha^{+1}}{Q_\\text{p}\\,\\omega_\\text{c}}$ |  $g^{-1}\\,\\alpha^{+2}$ | \n",
    "|$G>0$ | $\\frac{1}{\\omega_\\text{c}^2}$ | $\\frac{g^{+1/2}\\,\\alpha^{-1}}{Q_\\text{z}\\,\\omega_\\text{c}}$ | $g^{+1}\\,\\alpha^{-2}$ | $\\frac{1}{\\omega_\\text{c}^2}$ | $\\frac{\\alpha^{-1}}{Q_\\text{p}\\,\\omega_\\text{c}}$ | $\\alpha^{-2}$ |\n",
    "\n",
    "with $g=10^{\\frac{G}{20}}$, cut frequency $\\omega_c=2 \\pi f_c$ in rad/s, gain $G$ in dB, zero's quality $Q_z$ and pole's quality $Q_p$\n",
    "\n",
    "* **type I:**\n",
    "$\\alpha=1$ \n",
    "\n",
    "for $G\\gg 0$ cut frequency is at $G$-3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at $G$+3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\n",
    "* **type II:**\n",
    "$\\alpha=g^{+1/2}$\n",
    "\n",
    "for $G\\gg 0$ cut frequency is at +3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at -3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\t\t\n",
    "* **default: type III (one-half pad loss):**\n",
    "$\\alpha=g^{+1/4}$\n",
    "\n",
    "cut frequency is located at $G/2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [2.5330295910584447e-08 3.1793264965209052e-04 1.9952623149688793e+00]\n",
      "A = [2.5330295910584447e-08 1.5934378515892003e-04 5.0118723362727224e-01]\n",
      "b = [ 1.0671759979201019 -1.8570000365012005  0.8219339635255971]\n",
      "a = [ 1.                 -1.869022174734206   0.8770878232126937]\n"
     ]
    },
    {
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       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
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       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fc = 1000  # Hz\n",
    "G = 12  # dB\n",
    "B, A, b, a = audiofilter.biquad_lshv2nd(fc, G, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"highshv1st\"></a>\n",
    "### 1st Order High-Shelving `hshv1st`\n",
    "\n",
    "cf. \\cite{Christensen2003}, \\cite{Zoelzer2008}, \\cite{Zoelzer2011}\n",
    "\n",
    "| | $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| $G\\leq0$ | 0 | $\\frac{\\alpha^{+2}}{\\omega_\\text{c}}$ | 1 | 0 | $\\frac{g^{-1}\\,\\alpha^{+2}}{\\omega_\\text{c}}$ | 1 | \n",
    "| $G>0$ | 0 | $\\frac{g^{+1} \\,\\alpha^{-2}}{\\omega_\\text{c}}$ | 1 | 0  | $\\frac{\\alpha^{-2}}{\\omega_\\text{c}}$ | 1 |     \n",
    "\n",
    "with $g=10^{\\frac{G}{20}}$, cut frequency $\\omega_c=2 \\pi f_c$ in rad/s and gain $G$ in dB\n",
    "\n",
    "* **type I:**\n",
    "$\\alpha=1$ \n",
    "\n",
    "for $G\\gg 0$ cut frequency is at $G$-3 dB\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at $G$+3 dB\n",
    "\n",
    "* **type II:**\n",
    "$\\alpha=g^{+1/2}$\n",
    "\n",
    "for $G\\gg 0$ cut frequency is at +3 dB\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at -3 dB\n",
    "\t\t\n",
    "* **default: type III (one-half pad loss):**\n",
    "$\\alpha=g^{+1/4}$\n",
    "\n",
    "cut frequency is located at $G/2$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [0.0000000000000000e+00 3.1755586019227534e-04 1.0000000000000000e+00]\n",
      "A = [0.000000000000000e+00 7.976642564633298e-05 1.000000000000000e+00]\n",
      "b = [ 3.6363051987835404   0.23130373288995468 -3.405001465893586  ]\n",
      "a = [ 1.                   0.23130373288995468 -0.7686962671100454 ]\n"
     ]
    },
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       "   <rect height=\"157.5\" width=\"253.636364\" x=\"50.595312\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p1ae688028a\">\n",
       "   <rect height=\"157.5\" width=\"253.636364\" x=\"50.595312\" y=\"211.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p9dc921c312\">\n",
       "   <rect height=\"253.636364\" width=\"253.636364\" x=\"354.958949\" y=\"68.749943\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fc = 1000  # Hz\n",
    "G = 12  # dB\n",
    "B, A, b, a = audiofilter.biquad_hshv1st(fc, G, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"highshv2nd\"></a>\n",
    "### 2nd Order High-Shelving `hshv2nd`\n",
    "\n",
    "cf. \\cite{Bristow-Johnson1994}, \\cite{Christensen2003}, \\cite{Zoelzer2008}, \\cite{Zoelzer2011}\n",
    "\n",
    "| | $B_0$ | $B_1$ | $B_2$ | $A_0$ | $A_1$ | $A_2$ |\n",
    "| :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n",
    "| $G\\leq0$ | $\\frac{\\alpha^{+2}}{\\omega_\\text{c}^2}$ | $\\frac{\\alpha^{+1}}{Q_\\text{z}\\,\\omega_\\text{c}}$ | 1 | $\\frac{g^{-1}\\,\\alpha^{+2}}{\\omega_\\text{c}^2}$ | $\\frac{g^{-1/2}\\,\\alpha^{+1}}{Q_\\text{p}\\,\\omega_\\text{c}}$| 1 |\n",
    "| $G>0$ | $\\frac{g^{+1}\\,\\alpha^{-2}}{\\omega_\\text{c}^2}$ | $\\frac{g^{+1/2}\\,\\alpha^{-1}}{Q_\\text{z}\\,\\omega_\\text{c}}$ | 1 | $\\frac{\\alpha^{-2}}{\\omega_\\text{c}^2}$ | $\\frac{\\alpha^{-1}}{Q_\\text{p}\\,\\omega_\\text{c}}$ | 1 |\n",
    "\n",
    "with $g=10^{\\frac{G}{20}}$, cut frequency $\\omega_c=2 \\pi f_c$ in rad/s, gain $G$ in dB, zero's quality $Q_z$ and \n",
    "pole's quality $Q_p$\n",
    "\n",
    "* **type I:**\n",
    "$\\alpha=1$ \n",
    "\n",
    "for $G\\gg 0$ cut frequency is at $G$-3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at $G$+3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\n",
    "* **type II:**\n",
    "$\\alpha=g^{+1/2}$\n",
    "\n",
    "for $G\\gg 0$ cut frequency is at +3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\n",
    "for $G\\ll 0$ cut frequency is at -3 dB if $Q_p=Q_z=1/\\sqrt{2}$\n",
    "\t\t\n",
    "* **default: type III (one-half pad loss):**\n",
    "$\\alpha=g^{+1/4}$\n",
    "\n",
    "cut frequency is located at $G/2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = [5.054058485739946e-08 3.179326496520905e-04 1.000000000000000e+00]\n",
      "A = [1.2695220934386025e-08 1.5934378515892003e-04 1.0000000000000000e+00]\n",
      "b = [ 3.7304734301502065 -6.972337563207512   3.2719528204032353]\n",
      "a = [ 1.                 -1.7401066366938958  0.7701953240398256]\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<Figure size 960x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fc = 1000  # Hz\n",
    "G = 12  # dB\n",
    "B, A, b, a = audiofilter.biquad_hshv2nd(fc, G, fs)\n",
    "bode_plot(B, A, b, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises / Things To Think About\n",
    "\n",
    "1.) Check the differences of the types I,II vs. III for the PEQ and shelving filters with regard to their cut frequencies.\n",
    "\n",
    "Hints: \n",
    "\n",
    "* The **type III** filters as for PEQs and shelving filters consistently define the cut frequency as the point of half gain in dB.\n",
    "\n",
    "* Can you define the half gain $G/2$ cut frequencies of type III for small gain/attenuation $|G| <3$ dB?\n",
    "\n",
    "* Can you define the '3 dB cut frequencies' for small gain/attenuation $|G| <3$ dB for type I and II?\n",
    "\n",
    "* Where are the '3dB cut frequencies' located for type I,II for large gain or large attenuation? \n",
    "\n",
    "* Check how the filters of your favorite audio software are implemented.\n",
    "\n",
    "2.) Discuss the differences of the **sin**, **cos**, **tan**-style quality prewarping. For very high frequencies and rather small bandwidths the differences become obvious. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Different Types of High Shelve 2nd Order "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
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   "source": [
    "fc = 1000  # Hz\n",
    "G = 18  # dB\n",
    "B1, A1, b, a = audiofilter.biquad_hshv2nd(fc, G, fs, \"I\")  # fc at 15 dB\n",
    "B2, A2, b, a = audiofilter.biquad_hshv2nd(fc, G, fs, \"II\")  # fc at 3 dB\n",
    "B3, A3, b, a = audiofilter.biquad_hshv2nd(fc, G, fs, \"III\")  # fc at 9 dB\n",
    "f = np.arange(1, fs / 2, 1)\n",
    "s = 2 * np.pi * f\n",
    "s, H1 = signal.freqs(B1, A1, s)\n",
    "s, H2 = signal.freqs(B2, A2, s)\n",
    "s, H3 = signal.freqs(B3, A3, s)\n",
    "\n",
    "x = np.column_stack((f, f, f))\n",
    "y = np.column_stack((H1, H2, H3))\n",
    "title = \"High-Shelving Filter 2nd order\"\n",
    "legend = [\"type I\", \"type II\", \"type III\"]\n",
    "magnitude_plot(x, y, title, legend)"
   ]
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   "metadata": {},
   "source": [
    "#### Example: Different Types of PEQ 2nd Order for Boosting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BW = 2  # bandwidth in octaves\n",
    "fm = 2000  # mid frequency in Hz; using fm=1000 and BW=2, then fc is at 1 kHz\n",
    "G = 18  # dB\n",
    "QBP = audiofilter.q_from_bw(BW)\n",
    "B1, A1, b, a = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"I\")  # fc at 15 dB\n",
    "B2, A2, b, a = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"II\")  # fc at 15 dB\n",
    "B3, A3, b, a = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"III\")  # fc at 9 dB\n",
    "f = np.arange(1, fs / 2, 1)\n",
    "s = 2 * np.pi * f\n",
    "s, H1 = signal.freqs(B1, A1, s)\n",
    "s, H2 = signal.freqs(B2, A2, s)\n",
    "s, H3 = signal.freqs(B3, A3, s)\n",
    "np.testing.assert_allclose(H1, H2)  # type I and II are equal for boosting\n",
    "\n",
    "x = np.column_stack((f, f, f))\n",
    "y = np.column_stack((H1, H2, H3))\n",
    "title = \"PEQ 2nd order for boosting, type I == type II\"\n",
    "legend = [\"type I\", \"type II\", \"type III\"]\n",
    "magnitude_plot(x, y, title, legend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Different Types of PEQ 2nd Order for Cutting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
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CS2km3cI6KyQ1dkG9u2SJa8BHSYE8Ci5h5mI06hj3SZjoyzoVcNSI5HlLPWRwDuehgmVe+xskaM9nnudRTmDzR7Ew7uc5IWB4TqakGmN1PmcnjEYwcUJGQUrzmIByBhajfZgYU68VjFurxtku095ag/yhgV/3yaGbpzP7YwCx1VYlMV/O7I/95aAAMvbYvHymc1RJpIegBxbwfZzpHNEAxnM0H6vmpp1zAnpubGTilNXnaPT7sBnsz4ER0Rd6G8uZl6NQsOESPGs5nvgUDBmEH8B6Eubmg605CxnuyGeLYHY9d+ZSC8cEJpfPS2OOXURGcia20ApzX87yjyEVLV3BsG7sxLYcDrN5I3ujwlXb9pQCpteKtsTYG1TfExOxhayLfZzn8NjLlo3zPlp7RALQnHu7nqfaA4xpj53ss2fiF1uzZQbbOJ4Z9TpXWG20SmcVbGbtQwK6h+IxGvYuETvf+wcMSRjlcMvzKQh2w6yvjPyEIO6nJiiS1oWwJiG8UKSNFAtanWr6mcBgldBPa5j58UpNImMIQb5dvD5JZbXpp6g8Pd3/Lf0b3hO64yj3Y940+rhDYk9/5tPhsDobfnE55o39W8s2VdpBZOSuy3xk++BPX3/r4ptn7u37Z8/fux/evndPf/7ppx/fvDifAD/8MhG68293WP2iA/vdDvb1xtoPZgNZL9trY/wem563ZBFzwxFo2HEMD4Oc0995MTIngKXiSpjOK5+eBjHG8jMeo5QTht1hvBmkfe1g2EX2dOXGRdwzHQ0OzRk0sPlb1p5vNkplUTyIFzdereWLz8P9BnhuxPgpf3PFo9OdY+y9D2dPV1+9TYszWFrnNyvXsith+MvlscT6KUNerOevW6gWej/951/P3R/OcWbWm+XBfcTgPZqJIs46HMsVUxf5x5vL08N+7WLyDTbv7VhH8/lWVZRr1l/EH288BpMWZW37xfhvT/8HLDeABAplbmRzdHJlYW0KZW5kb2JqCjExIDAgb2JqCjQwMTgKZW5kb2JqCjE2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggODggPj4Kc3RyZWFtCnicPY25EcAwCARzqqAEgXikfjyO5P5Tn/ATADvs3Fy6cmNNrFTHTD6EJGbhRRqjaJFKY+sN5Pg9FBqv/cKwo/N2Nqyuo6FbgmTaR8htV73rr1t03skLG84KZW5kc3RyZWFtCmVuZG9iagoxNyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE0NCA+PgpzdHJlYW0KeJw9jzsSAyEMQ3tOoSPgP5xnM6k292+jJZAGv7GwJVsoOnLw8Rqo7HhJO/hpnk41cDdjb5PHIlNBsmu9kBm4mk5FcqMOKjqh5Yi5FO4JL0676Cabk6YPacgmiSfK3fJXJI9QsWGMPS51VgrtYkWTaUinsTAijdUTxZgMwOHib9Ncpxl/PvX6H3u39xdMuDPWCmVuZHN0cmVhbQplbmRvYmoKMTQgMCBvYmoKPDwgL0Jhc2VGb250IC9EZWphVnVTYW5zLU9ibGlxdWUgL0NoYXJQcm9jcyAxNSAwIFIKL0VuY29kaW5nIDw8IC9EaWZmZXJlbmNlcyBbIDcyIC9IIDEwMiAvZiBdIC9UeXBlIC9FbmNvZGluZyA+PiAvRmlyc3RDaGFyIDAKL0ZvbnRCQm94IFsgLTEwMTYgLTM1MSAxNjYwIDEwNjggXSAvRm9udERlc2NyaXB0b3IgMTMgMCBSCi9Gb250TWF0cml4IFsgMC4wMDEgMCAwIDAuMDAxIDAgMCBdIC9MYXN0Q2hhciAyNTUgL05hbWUgL0RlamFWdVNhbnMtT2JsaXF1ZQovU3VidHlwZSAvVHlwZTMgL1R5cGUgL0ZvbnQgL1dpZHRocyAxMiAwIFIgPj4KZW5kb2JqCjEzIDAgb2JqCjw8IC9Bc2NlbnQgOTI5IC9DYXBIZWlnaHQgMCAvRGVzY2VudCAtMjM2IC9GbGFncyA5NgovRm9udEJCb3ggWyAtMTAxNiAtMzUxIDE2NjAgMTA2OCBdIC9Gb250TmFtZSAvRGVqYVZ1U2Fucy1PYmxpcXVlCi9JdGFsaWNBbmdsZSAwIC9NYXhXaWR0aCAxMzUwIC9TdGVtViAwIC9UeXBlIC9Gb250RGVzY3JpcHRvciAvWEhlaWdodCAwID4+CmVuZG9iagoxMiAwIG9iagpbIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwCjYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgMzE4IDQwMSA0NjAgODM4IDYzNgo5NTAgNzgwIDI3NSAzOTAgMzkwIDUwMCA4MzggMzE4IDM2MSAzMTggMzM3IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYKNjM2IDYzNiAzMzcgMzM3IDgzOCA4MzggODM4IDUzMSAxMDAwIDY4NCA2ODYgNjk4IDc3MCA2MzIgNTc1IDc3NSA3NTIgMjk1CjI5NSA2NTYgNTU3IDg2MyA3NDggNzg3IDYwMyA3ODcgNjk1IDYzNSA2MTEgNzMyIDY4NCA5ODkgNjg1IDYxMSA2ODUgMzkwIDMzNwozOTAgODM4IDUwMCA1MDAgNjEzIDYzNSA1NTAgNjM1IDYxNSAzNTIgNjM1IDYzNCAyNzggMjc4IDU3OSAyNzggOTc0IDYzNCA2MTIKNjM1IDYzNSA0MTEgNTIxIDM5MiA2MzQgNTkyIDgxOCA1OTIgNTkyIDUyNSA2MzYgMzM3IDYzNiA4MzggNjAwIDYzNiA2MDAgMzE4CjM1MiA1MTggMTAwMCA1MDAgNTAwIDUwMCAxMzUwIDYzNSA0MDAgMTA3MCA2MDAgNjg1IDYwMCA2MDAgMzE4IDMxOCA1MTggNTE4CjU5MCA1MDAgMTAwMCA1MDAgMTAwMCA1MjEgNDAwIDEwMjggNjAwIDUyNSA2MTEgMzE4IDQwMSA2MzYgNjM2IDYzNiA2MzYgMzM3CjUwMCA1MDAgMTAwMCA0NzEgNjE3IDgzOCAzNjEgMTAwMCA1MDAgNTAwIDgzOCA0MDEgNDAxIDUwMCA2MzYgNjM2IDMxOCA1MDAKNDAxIDQ3MSA2MTcgOTY5IDk2OSA5NjkgNTMxIDY4NCA2ODQgNjg0IDY4NCA2ODQgNjg0IDk3NCA2OTggNjMyIDYzMiA2MzIgNjMyCjI5NSAyOTUgMjk1IDI5NSA3NzUgNzQ4IDc4NyA3ODcgNzg3IDc4NyA3ODcgODM4IDc4NyA3MzIgNzMyIDczMiA3MzIgNjExIDYwOAo2MzAgNjEzIDYxMyA2MTMgNjEzIDYxMyA2MTMgOTk1IDU1MCA2MTUgNjE1IDYxNSA2MTUgMjc4IDI3OCAyNzggMjc4IDYxMiA2MzQKNjEyIDYxMiA2MTIgNjEyIDYxMiA4MzggNjEyIDYzNCA2MzQgNjM0IDYzNCA1OTIgNjM1IDU5MiBdCmVuZG9iagoxNSAwIG9iago8PCAvSCAxNiAwIFIgL2YgMTcgMCBSID4+CmVuZG9iagoyMiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI1OSA+PgpzdHJlYW0KeJw9UklywzAMu/sVfAJ3Se9Jpyfn/9cC9NSXEGOKAAimd4vK2fhpK1l+5McuO0sit3wHbZP7iqoHpG6CzCXHJVeIWcrnSpBYtJSZWJ+pDsrPNahV+MJPzExMhyQRS8hJPYqwfl4H96B+vaTzW2T8o2OD0luSTAWdGu6Vo5TYsFSfGuQeNN2UVp+ZdmUHLI03ZKUmdfr10+MHSzClLxLRQYjEn+RyhywLKQfxdq7eQHhXuyDVUysPO0Saj5HeUgWrOTMBS0bTDiNgbdaYIFUCvEVrCLQW4vKFTisiPjk3dDBNVZ6FyLBS4Vh7z2gNF7qGvNJwepJx//kfvCve1+8f2vNmZAplbmRzdHJlYW0KZW5kb2JqCjIzIDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNzkgPj4Kc3RyZWFtCnicTc27DcAgDATQnik8AuD/PlGqsH8bGyJCYz/pTjrBDhXc4rAYaHe4WvGlUZh96pkSklBzPURYMyU6hKRf+ssww5jYyLbvt1buF94bHBkKZW5kc3RyZWFtCmVuZG9iagoyNCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDc3ID4+CnN0cmVhbQp4nDM3NVIwULC0ABJmpiYK5kaWCimGXEA+iJXLZWhpDmblgFkmxgZAlqmpKRILIgvTC2HB5GC0sYk51AQECyQHtjYHZlsOVxoAnuAbmgplbmRzdHJlYW0KZW5kb2JqCjI1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNDkgPj4Kc3RyZWFtCnicM7I0VTBQsLQAEoaW5grmRpYKKYZcQD6IlcsFE8sBswyANFhpDkxFDlcaAKVEDOQKZW5kc3RyZWFtCmVuZG9iagoyNiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE2NSA+PgpzdHJlYW0KeJxFjzsSAyEMQ3tOoSOAf8B5NpOKvX8byztJGiyMJT+iKzr2ysNjY8rGa7SxJ8IW7lI6DaepjK+Kp2ddoMthMlNvXM1cYKqwyG5OsfoYfKHy7OaEr1WeGMKXTAkNMJU7uYf1+lGclnwkuwuC6pSNysIwR9L3QExNm6eFgfyPL3lqQVCZ5o1rlpVHaxVTNGeYKlsLgvWBoDql+gPT/0ynvT/c9D2ACmVuZHN0cmVhbQplbmRvYmoKMjcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNTEgPj4Kc3RyZWFtCnicNVE7cgUxCOt9Ci6wMwZjsM/zMqmS+7eRINssWj5CwnlSpuyQR+1ILpV0ky8d67pEmPyOZVbIYkusLWZL9jH5DD0qG2MaUxwcjCucFSBLE3bovTWjHqiQ5Zo0qfQWpJ3kATZjdYOk22NGEYRlETL2CiIuZQdFcKZlkYRCm9PktYLKgqQFT/wtxz9j+3qhY+hRJTIv5FqXQZwVIXR6oQVRD7hIzghnVwvZhF/Y9iPnIn/gYCdvbE6Z//oBPK+gurO7Y7Gd4znh9vZbcAEjVt8otDOrg/09k3MWC9+PpIy9hciYUYcwXOvM97L4cjlIHc/Yl/mM7z9r1GLuCmVuZHN0cmVhbQplbmRvYmoKMjggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA1NCA+PgpzdHJlYW0KeJwzNjZXMFAwNDJX0DUyNlUwMjRQMDczUUgx5IIxc8EssGwOF1whhAmSz4GrzOFKAwBMkA8VCmVuZHN0cmVhbQplbmRvYmoKMjkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMzAgPj4Kc3RyZWFtCnicNVFJbsMwDLzrFfOBAOIuv8dBT+3/rx3SCWBgaEuczREbGxF4icHPQeTGW9aMmvibyV3xuzwVHgm3gidRBF6Ge9kJLm8Yl/04zHzwXlo5kxpPMiAX2fTwRMhgl0DowOwa1GGbaSf6hoTPjkg1G1lOX0vQS6sQKE/ZfqcLSrSt6s/tsy607WtPONntqSeVTyCeW7ICl41XTBZjGfRE5S7F9EGqs4WehPKifA6y+aghEl2inIEnBgejQDuw57afiVeFoHV1n7aNoRopHU//NjQ1SSLkEyWc2dK4W/j+nnv9/AOmVFOfCmVuZHN0cmVhbQplbmRvYmoKMzAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMjcgPj4Kc3RyZWFtCnicNU87sgMhDOs5hS6QGYxtYM+zmVQv92+fZLINEv5I8vRERyZe5sgIrNnxthYZiBn4FlPxrz3tw4TqPbiHCOXiQphhJJw167ibp+PFv13lM9bBuw2+YpYXBLYwk/WVxZnLdsFYGidxTrIbY9dEbGNd6+kU1hFMKAMhne0wJcgcFSl9sqOMOTpO5InnYqrFLr/vYX3BpjGiwhxXBU/QZFCWPe8moB0X9N/Vjd9JNIteAjKRYGGdJObOWU741WtHx1GLIjEnpBnkMhHSnK5iCqEJxTo7CioVBZfqc8rdPv9oXVtNCmVuZHN0cmVhbQplbmRvYmoKMzEgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNDUgPj4Kc3RyZWFtCnicRVC7jUMxDOs9BRcIYP0se553SJXbvz1KRnCFIVo/kloSmIjASwyxlG/iR0ZBPQu/F4XiM8TPF4VBzoSkQJz1GRCZeIbaRm7odnDOvMMzjDkCF8VacKbTmfZc2OScBycQzm2U8YxCuklUFXFUn3FM8aqyz43XgaW1bLPTkewhjYRLSSUml35TKv+0KVsq6NpFE7BI5IGTTTThLD9DkmLMoJRR9zC1jvRxspFHddDJ2Zw5LZnZ7qftTHwPWCaZUeUpnecyPiep81xOfe6zHdHkoqVV+5z93pGW8iK126HV6VclUZmN1aeQuDz/jJ/x/gOOoFk+CmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzOTIgPj4Kc3RyZWFtCnicPVJLbgUxCNvPKbhApfBNcp6p3u7df1ubzFSqCi8DtjGUlwypJT/qkogzTH71cl3iUfK9bGpn5iHuLjam+FhyX7qG2HLRmmKxTxzJL8i0VFihVt2jQ/GFKBMPAC3ggQXhvhz/8ReowdewhXLDe2QCYErUbkDGQ9EZSFlBEWH7kRXopFCvbOHvKCBX1KyFoXRiiA2WACm+qw2JmKjZoIeElZKqHdLxjKTwW8FdiWFQW1vbBHhm0BDZ3pGNETPt0RlxWRFrPz3po1EytVEZD01nfPHdMlLz0RXopNLI3cpDZ89CJ2Ak5kmY53Aj4Z7bQQsx9HGvlk9s95gpVpHwBTvKAQO9/d6Sjc974CyMXNvsTCfw0WmnHBOtvh5i/YM/bEubXMcrh0UUqLwoCH7XQRNxfFjF92SjRHe0AdYjE9VoJRAMEsLO7TDyeMZ52d4VtOb0RGijRB7UjhE9KLLF5ZwVsKf8rM2xHJ4PJntvtI+UzMyohBXUdnqots9jHdR3nvv6/AEuAKEZCmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzMgPj4Kc3RyZWFtCnicTY9BEsMwCAPvfoWegLEB8550ekr+fy2QNu4F7YyAkYYwCDxiDOswJbx6++FVpEtwNo75JRlFPAhqC9wXVAVHY4qd+Njdoeyl4ukUTYvrEXPTtKR0N1Eqbb2dyPjAfZ/eH1W2JJ2CHlvqhC7RJPJFAnPYVDDP6sZLS4+n7dneH2Y+M9cKZW5kc3RyZWFtCmVuZG9iagozNCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0NyA+PgpzdHJlYW0KeJxNUbttRDEM698UXOAA62t5ngtSXfZvQ8kIkMIgoS8ppyUW9sZLDOEHWw++5JFVQ38ePzHsMyw9yeTUP+a5yVQUvhWqm5hQF2Lh/WgEvBZ0LyIrygffj2UMc8734KMQl2AmNGCsb0kmF9W8M2TCiaGOw0GbVBh3TRQsrhXNM8jtVjeyOrMgbHglE+LGAEQE2ReQzWCjjLGVkMVyHqgKkgVaYNfpG1GLgiuU1gl0otbEuszgq+f2djdDL/LgqLp4fQzrS7DC6KV7LHyuQh/M9Ew7d0kjvfCmExFmDwVSmZ2RlTo9Yn23QP+fZSv4+8nP8/0LFShcKgplbmRzdHJlYW0KZW5kb2JqCjM1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzM4ID4+CnN0cmVhbQp4nEVSS3LFMAjb5xRcIDPmZ+PzvE5X6f23lXA63Tz0DAgJMj1lSKbcNpZkhOQc8qVXZIjVkJ9GjkTEEN8pocCu8rm8lsRcyG6JSvGhHT+XpTcyza7QqrdHpzaLRjUrI+cgQ4R6VujM7lHbZMPrdiHpOlMWh3As/0MFspR1yimUBG1B39gj6G8WPBHcBrPmcrO5TG71v+5bC57XOluxbQdACZZz3mAGAMTDCdoAxNza3hYpKB9VuopJwq3yXCc7ULbQqnS8N4AZBxg5YMOSrQ7XaG8Awz4P9KJGxfYVoKgsIP7O2WbB3jHJSLAn5gZOPXE6xZFwSTjGAkCKreIUuvEd2OIvF66ImvAJdTplTbzCntrix0KTCO9ScQLwIhtuXR1FtWxP5wm0PyqSM2KkHsTRCZHUks4RFJcG9dAa+7iJGa+NxOaevt0/wjmf6/sXFriD4AplbmRzdHJlYW0KZW5kb2JqCjM2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNjggPj4Kc3RyZWFtCnicMzK3UDBQsDQBEoYWJgrmZgYKKYZcQL6piblCLhdIDMTKAbMMgLQlnIKIW0I0QZSCWBClZiZmEEk4AyKXBgDJtBXlCmVuZHN0cmVhbQplbmRvYmoKMzcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MSA+PgpzdHJlYW0KeJw9zLsVgDAIBdA+U7wRQnyA7OOx0v1bwUQbuHzVAx0hGdQNbh2HtKxLd5N96nq1iaTIgNJTalwaToyoaX2pfWrguxvmS9WJP83P5wOHxxlrCmVuZHN0cmVhbQplbmRvYmoKMzggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA0NSA+PgpzdHJlYW0KeJwzMrdQMFCwNAEShhYmCuZmBgophlyWEFYuF0wsB8wC0ZZwCiKeBgCffQy1CmVuZHN0cmVhbQplbmRvYmoKMzkgMCBvYmoKPDwgL0JCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzcKL1N1YnR5cGUgL0Zvcm0gL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnic4zI0MFMwNjVVyOUyNzYCs3LALCNzIyALJItgQWTTAAFfCgoKZW5kc3RyZWFtCmVuZG9iago0MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE2MSA+PgpzdHJlYW0KeJxFkEsSwyAMQ/ecQkfwRwZ8nnS6Su+/rSFNs4CnsUAGdycEqbUFE9EFL21Lugs+WwnOxnjoNm41EuQEdYBWpONolFJ9ucVplXTxaDZzKwutEx1mDnqUoxmgEDoV3u2i5HKm7s75R3D1X/VHse6czcTAZOUOhGb1Ke58mx1RXd1kf9JjbtZrfxX2qrC0rKXlhNvOXTOgBO6pHO39BalzOoQKZW5kc3RyZWFtCmVuZG9iago0MSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMyMCA+PgpzdHJlYW0KeJw1UbtxxTAM6zUFF/Cd+JU0j3Ovytu/DUA7FWEaBECqvGRKuVzqklWywuRHh+oUTfk+YKb8DvWQ4+ge2SG6U9aWexgIy8Q8pY5YTZZ7uAWBLwxNibmF8/cI6CsGozATgbr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      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BW = 2  # bandwidth in octaves\n",
    "fm = 2000  # mid frequency in Hz; using fm=1000 and BW=2, then fc is at 1 kHz\n",
    "G = -18  # dB\n",
    "QBP = audiofilter.q_from_bw(BW)\n",
    "B1, A1, b, a = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"I\")  # fc at -3dB\n",
    "B2, A2, b, a = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"II\")  # fc at -15dB\n",
    "B3, A3, b, a = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"III\")  # fc at -9dB\n",
    "f = np.arange(1, fs / 2, 1)\n",
    "s = 2 * np.pi * f\n",
    "s, H1 = signal.freqs(B1, A1, s)\n",
    "s, H2 = signal.freqs(B2, A2, s)\n",
    "s, H3 = signal.freqs(B3, A3, s)\n",
    "\n",
    "x = np.column_stack((f, f, f))\n",
    "y = np.column_stack((H1, H2, H3))\n",
    "title = \"PEQ 2nd order for cutting\"\n",
    "legend = [\"type I\", \"type II\", \"type III\"]\n",
    "magnitude_plot(x, y, title, legend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Different Types for Quality Prewarping for PEQ 2nd Order "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
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   "source": [
    "BW = 2  # bandwidth in octaves\n",
    "fm = 12000  # Hz\n",
    "G = 18  # dB\n",
    "QBP = audiofilter.q_from_bw(BW)\n",
    "B, A, bsin, asin = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"III\", \"sin\")\n",
    "B, A, bcos, acos = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"III\", \"cos\")\n",
    "B, A, btan, atan = audiofilter.biquad_peq2nd(fm, G, QBP, fs, \"III\", \"tan\")\n",
    "f = np.arange(1, fs / 2, 1)\n",
    "s = 2 * np.pi * f\n",
    "W = s / fs\n",
    "s, H = signal.freqs(B, A, 2 * np.pi * f)\n",
    "W, Hsin = signal.freqz(bsin, asin, W)\n",
    "W, Hcos = signal.freqz(bcos, acos, W)\n",
    "W, Htan = signal.freqz(btan, atan, W)\n",
    "\n",
    "x = np.column_stack((f, f, f, f))\n",
    "y = np.column_stack((H, Hsin, Hcos, Htan))\n",
    "title = \"PEQ 2nd order\"\n",
    "legend = [\"Analog\", \"sin Q-warp\", \"cos Q-warp\", \"tan Q-warp\"]\n",
    "magnitude_plot(x, y, title, legend)"
   ]
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   "source": [
    "### Short Excursus: Higher Order Filters\n",
    "\n",
    "In audio signal processing also IIR filters of higher order are applied. However, they will be usually split into second order sections for series or parallel connection.\n",
    "The [Shelving Filter Cascade with Adjustable Transition Slope and Bandwidth](http://www.aes.org/e-lib/browse.cfm?elib=20756) is one example for a series connection, check the [open source code](https://github.com/spatialaudio/aes148-shelving-filter).\n",
    "\n",
    "Another prominent example of using higher order IIR filters is found in loudspeaker engineering. For a multi-way loudspeaker each driver must only be driven within an appropriate intended frequency range. This is usually realized with a bandpass filter that is built from a series connection of a higher order lowpass and a higher order highpass filter. Thus, each loudspeaker exhibits its own bandpass filter. The acoustic summation of all the driver's generated sound pressures then yields the desired full audio bandwidth in the sonic domain.\n",
    "\n",
    "Note that the group delay of an IIR filter increases with higher filter order. \n",
    "\n",
    "#### Linkwitz-Riley Crossover\n",
    "\n",
    "Consider the following two driver application, in which the same bandpass characteristic is used for the low (LF) and high (HF) frequency driver. A special and often used case is achieved, when **two equal** 2nd-order **Butterworth** high-/low-pass filters **in series** built a 4th-order so called **[Linkwitz-Riley](http://www.linkwitzlab.com/crossovers.htm)** high-/low-pass filter."
   ]
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   "source": [
    "f = np.arange(1, fs / 2, 1)\n",
    "s = 2 * np.pi * f\n",
    "bi = 1\n",
    "ai = np.sqrt(2)  # Butterworth\n",
    "\n",
    "# low frequency driver range\n",
    "fLow_HP = 20\n",
    "fLow_LP = 1000\n",
    "# high frequency driver range\n",
    "fHigh_HP = fLow_LP\n",
    "fHigh_LP = 15000\n",
    "\n",
    "# LOW frequency driver -> highpass\n",
    "B, A, b, a = audiofilter.biquad_hp2nd(fLow_HP, fs, bi, ai)\n",
    "s, LF_HP = signal.freqs(B, A, s)\n",
    "# LOW frequency driver -> lowpass\n",
    "B, A, b, a = audiofilter.biquad_lp2nd(fLow_LP, fs, bi, ai)\n",
    "s, LF_LP = signal.freqs(B, A, s)\n",
    "# HIGH frequency driver -> highpass\n",
    "B, A, b, a = audiofilter.biquad_hp2nd(fHigh_HP, fs, bi, ai)\n",
    "s, HF_HP = signal.freqs(B, A, s)\n",
    "# HIGH frequency driver -> lowpass\n",
    "B, A, b, a = audiofilter.biquad_lp2nd(fHigh_LP, fs, bi, ai)\n",
    "s, HF_LP = signal.freqs(B, A, s)\n",
    "\n",
    "# Butterworth Lowpass^2 * Butterwoth Highpass^2\n",
    "# results in a Linkwitz-Riley Bandpass:\n",
    "LF = (LF_HP * LF_HP) * (LF_LP * LF_LP)\n",
    "HF = (HF_HP * HF_HP) * (HF_LP * HF_LP)\n",
    "LF[0] = 1e-15  # avoid zero at DC\n",
    "HF[0] = 1e-15  # avoid zero at DC\n",
    "# simulation of the acoustic summation on both driver's middle axis:\n",
    "AcousticSum = LF + HF\n",
    "\n",
    "x = np.column_stack((f, f, f))\n",
    "y = np.column_stack((LF, HF, AcousticSum))\n",
    "title = \"4th-order Linkwitz-Riley X-Over for a Two-Way Loudspeaker\"\n",
    "legend = [\n",
    "    \"electric bandpass for low frequency driver\",\n",
    "    \"electric bandpass for high frequency driver\",\n",
    "    \"acoustic on-axis summation\",\n",
    "]\n",
    "magnitude_plot(x, y, title, legend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "* What filter characteristic has the acoustic sum? To explore it in detail, plot and discuss the phase of the Linwitz-Riley filters as well as of the acoustic sum.\n",
    "\n",
    "* Why sum the magnitudes of the low and the high frequency driver precisely to 0 dB at $f_c$ for the chosen example? Hints: Which phase shift exhibits the sum transfer function? What is the magnitude of the low and high frequency driver bandpass exactly at the crossover frequency?\n",
    "\n",
    "* Is this handling also possible with normal Butterworth filters? Why?\n",
    "\n",
    "* What happens for a 6th-order Linkwitz-Riley Crossver, i.e. built from 3rd-order Butterworth filters? See the coefficients of a 3rd-order BW filter below. Pay special attention to the phase and polarity of the LF and HF driver!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Appendix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Butterworth Filter Characteristics\n",
    "\n",
    "Higher order filter design can be realized with series connection of biquads. The coefficients for **Butterworth** type are e.g. given as, cf. \\cite{TietzeSchenk2008} \n",
    "\n",
    "$\\text{a}_\\text{i}$ $\\text{b}_\\text{i}$     \n",
    "\n",
    "**1st order**\n",
    "\n",
    "1.0000 0.0000 \n",
    "\n",
    "**2nd order**\n",
    "\n",
    "1.4142 1.0000 (used in the example above)\n",
    "\n",
    "**3rd order** (2 biquads in series connection with different bi, ai)\n",
    "\n",
    "1.0000 0.0000\n",
    "\n",
    "1.0000 1.0000\n",
    "\n",
    "**4th order** (2 biquads in series connection with different bi, ai)\n",
    "\n",
    "1.8478 1.0000 \n",
    "\n",
    "0.7654 1.0000\n",
    "\n",
    "Other common filter characteristics are Bessel, Elliptic, Chebychev."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Zoelzer PEQ (Type II, no Q prewarp)\n",
    "We check type of \\cite[Table 2.4]{Zoelzer2011} # U. Zoelzer (2011): \"DAFX - Digital Audio Effects\", 2nd, Wiley, Table 2.4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "fm = 1000\n",
    "Q = 2 / 3\n",
    "G = 12\n",
    "B, A, b, a = audiofilter.biquad_peq2nd(\n",
    "    fm, G, Q, fs, filter_type=\"II\", q_warp_method=\"NoQPreWarp\"\n",
    ")\n",
    "bZ, aZ = audiofilter.biquad_peq2nd_zoelzer(fm, G, Q, fs)\n",
    "np.testing.assert_allclose(bZ, b)\n",
    "np.testing.assert_allclose(aZ, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RBJ PEQ (Type III, Q prewarp: sin)\n",
    "We check type \\cite(Bristow-Johnson1994), eq. (16)\n",
    "\n",
    "Robert Bristow-Johnson (1994): \"The equivalence of various methods of\n",
    "computing biquad coefficients for audio parametric equalizers.\"\n",
    "In: Proc. of 97th AES Convention, San Fransisco, eq. (16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "fm = 1000\n",
    "Q = 2 / 3\n",
    "G = 12\n",
    "B, A, b, a = audiofilter.biquad_peq2nd(\n",
    "    fm, G, Q, fs, filter_type=\"III\", q_warp_method=\"sin\"\n",
    ")\n",
    "bR, aR = audiofilter.biquad_peq2nd_RBJ(fm, G, Q, fs)\n",
    "np.testing.assert_allclose(bR, b)\n",
    "np.testing.assert_allclose(aR, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Zoelzer 2nd Order Low-Shelving (Type I, Qz=Qp=1/sqrt(2))\n",
    "We check type of \\cite[Table 2.3]{Zoelzer2011} # U. Zoelzer (2011): \"DAFX - Digital Audio Effects\", 2nd, Wiley, Table 2.3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "fc = 1000\n",
    "G = 12\n",
    "B, A, b, a = audiofilter.biquad_lshv2nd(\n",
    "    fc, G, fs, filter_type=\"I\", qz=1 / np.sqrt(2), qp=1 / np.sqrt(2)\n",
    ")\n",
    "bZ, aZ = audiofilter.biquad_lshv2nd_Zoelzer(fc, G, fs)\n",
    "np.testing.assert_allclose(bZ, b)\n",
    "np.testing.assert_allclose(aZ, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RBJ 2nd Order Low-Shelving (Type III, Qz=Qp=1/sqrt(2) -> S = 1)\n",
    "We check type of Robert Bristow-Johnson [Audio EQ Cookbook](http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "fc = 1000\n",
    "G = 1\n",
    "S = 1\n",
    "B, A, b, a = audiofilter.biquad_lshv2nd(\n",
    "    fc, G, fs, filter_type=\"III\", qz=1 / np.sqrt(2), qp=1 / np.sqrt(2)\n",
    ")\n",
    "bR, aR = audiofilter.biquad_lshv2nd_RBJ(fc, G, S, fs)\n",
    "np.testing.assert_allclose(bR, b)\n",
    "np.testing.assert_allclose(aR, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Zoelzer 2nd Order High-Shelving (Type I, Qz=Qp=1/sqrt(2))\n",
    "We check type of \\cite[Table 2.3]{Zoelzer2011} # U. Zoelzer (2011): \"DAFX - Digital Audio Effects\", 2nd, Wiley, Table 2.3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "fc = 1000\n",
    "G = 12\n",
    "B, A, b, a = audiofilter.biquad_hshv2nd(\n",
    "    fc, G, fs, filter_type=\"I\", qz=1 / np.sqrt(2), qp=1 / np.sqrt(2)\n",
    ")\n",
    "bZ, aZ = audiofilter.biquad_hshv2nd_Zoelzer(fc, G, fs)\n",
    "np.testing.assert_allclose(bZ, b)\n",
    "np.testing.assert_allclose(aZ, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RBJ 2nd Order High-Shelving (Type III, Qz=Qp=1/sqrt(2) -> S = 1)\n",
    "We check type of Robert Bristow-Johnson [Audio EQ Cookbook](http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "fc = 1000\n",
    "G = 12\n",
    "S = 1\n",
    "B, A, b, a = audiofilter.biquad_hshv2nd(\n",
    "    fc, G, fs, filter_type=\"III\", qz=1 / np.sqrt(2), qp=1 / np.sqrt(2)\n",
    ")\n",
    "bR, aR = audiofilter.biquad_hshv2nd_RBJ(fc, G, S, fs)\n",
    "np.testing.assert_allclose(bR, b)\n",
    "np.testing.assert_allclose(aR, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "Please see the [biblio.bib](biblio.bib) for the cited references."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
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