{ "cells": [ { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "# Realization of Recursive 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).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quantization of Filter Coefficients\n", "\n", "The finite numerical resolution of digital number representations has impact on the properties of filters, as already discussed for [non-recursive filters](../nonrecursive_filters/quantization_effects.ipynb#Quantization-Effects). The quantization of coefficients, state variables, algebraic operations and signals plays an important role in the design of recursive filters. Compared to non-recursive filters, the impact of quantization is often more prominent due to the feedback. Severe degradations from the desired characteristics and instability are potential consequences of a finite word length in practical implementations.\n", "\n", "A recursive filter of order $N \\geq 2$ can be [decomposed into second-order sections (SOS)](../recursive_filters/cascaded_structures.ipynb). Due to the grouping of poles/zeros to filter coefficients with a limited amplitude range, a realization by cascaded SOS is favorable in practice. We therefore limit our investigation of quantization effects to SOS. The transfer function of a SOS is given as\n", "\n", "\\begin{equation}\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", "This can be [split into a non-recursive part and a recursive part](../recursive_filters/introduction.ipynb#Recursive-Filters). The quantization effects of non-recursive filters have already been discussed. We therefore focus here on the recursive part given by the transfer function\n", "\n", "\\begin{equation}\n", "H(z) = \\frac{1}{1 + a_1 z^{-1} + a_2 z^{-2}}\n", "\\end{equation}\n", "\n", "This section investigates the consequences of quantization in recursive filters. As for non-recursive filters, we first take a look at the quantization of filter coefficients. The structure used for the realization of the filter has impact on the quantization effects. We begin with the direct form followed by the coupled form, as example for an alternative structure." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Direct Form\n", "\n", "Above transfer function of the recursive part of a SOS can be rewritten in terms of its complex conjugate poles $z_{\\infty}$ and $z_{\\infty}^*$ as\n", "\n", "\\begin{equation}\n", "H(z) = \\frac{1}{(z-z_{\\infty}) (z-z_{\\infty}^*)} = \\frac{z^{-2}}{ 1 \\underbrace{- 2 r \\cos(\\varphi)}_{a_1} \\; z^{-1} + \\underbrace{r^2}_{a_2} \\; z^{-2} }\n", "\\end{equation}\n", "\n", "where $r = |z_{\\infty}|$ and $\\varphi = \\arg \\{z_{\\infty}\\}$ denote the absolute value and phase of the pole $z_{\\infty}$, respectively. Let's assume a [linear uniform quantization](../quantization/linear_uniform_quantization_error.ipynb#Quantization-Error-of-a-Linear-Uniform-Quantizer) of the coefficients $a_1$ and $a_2$ with quantization step $Q$. Discarding clipping, the following relations for the locations of the poles can be found\n", "\n", "\\begin{align}\n", "r_n &= \\sqrt{n \\cdot Q} \\\\\n", "\\varphi_{nm} &= \\arccos \\left( \\sqrt{\\frac{m^2 Q}{4 n}} \\right)\n", "\\end{align}\n", "for $n \\in \\mathbb{N}_0$ and $m \\in \\mathbb{Z}$. Quantization of the filter coefficients $a_1$ and $a_2$ into a finite number of amplitude values leads to a finite number of pole locations. In the $z$-plane the possible pole locations are given by the intersections of\n", "\n", "* circles whose radii $r_n$ are given by $r_n = \\sqrt{n \\cdot Q}$ with\n", "* equidistant vertical lines which intersect the horizontal axis at $\\frac{1}{2} m \\cdot Q$.\n", "\n", "The finite number of pole locations may lead to deviations from a desired filter characteristic since a desired pole location is moved to the next possible pole location. The filter may even get unstable, when poles are moved outside the unit circle. For illustration, the resulting pole locations for a SOS realized in direct form are computed and plotted." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.patches import Circle\n", "import scipy.signal as sig\n", "import itertools\n", "\n", "\n", "def compute_pole_locations(Q):\n", " a1 = np.arange(-2, 2+Q, Q)\n", " a2 = np.arange(0, 1+Q, Q)\n", " \n", " p = np.asarray([np.roots([1, n, m]) for (n,m) in itertools.product(a1, a2)])\n", " p = p[np.imag(p)!=0]\n", "\n", " return p\n", "\n", "\n", "def plot_pole_locations(p, Q):\n", " ax = plt.gca()\n", " for n in np.arange(np.ceil(2/Q)+1):\n", " circle = Circle((0,0), radius=np.sqrt(n*Q), fill=False, color='black', ls='solid', alpha=0.05)\n", " ax.add_patch(circle)\n", " ax.axvline(.5*n*Q, color='0.95')\n", " ax.axvline(-.5*n*Q, color='0.95')\n", "\n", " unit_circle = Circle((0,0), radius=1, fill=False, color='red', ls='solid')\n", " ax.add_patch(unit_circle) \n", "\n", " plt.plot(np.real(p), np.imag(p), 'b.', ms = 4)\n", " plt.xlabel(r'Re{$z$}')\n", " plt.ylabel(r'Im{$z$}')\n", " plt.axis([-1.1, 1.1, -1.1, 1.1])\n", "\n", "# compute and plot pole locations\n", "for w in [5,6]:\n", " Q = 2/(2**(w-1)) # quantization stepsize\n", " plt.figure(figsize=(5, 5))\n", " p = compute_pole_locations(Q)\n", " plot_pole_locations(p, Q)\n", " plt.title(r'Direct form coefficient quantization to $w=%d$ bits'%w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* What consequences does the distribution of pole locations on the desired characteristics of a filter have for e.g. low/high frequencies?\n", "\n", "Solution: Quantization of the original filter coefficients leads to a limited number of possible pole and zero locations. These locations are not uniformly distributed over the $z$-plane, as can be observed from above illustrations. The density of potential locations is especially low for low frequencies and close to the Nyquist frequency. The properties of a designed filter having poles and/or zeros at low/high frequencies will potentially deviate more when quantizing its coefficients, as a consequence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coupled Form\n", "\n", "Besides the quantization step $Q$, the pole distribution depends also on the topology of the filter. In order to gain a different distribution of pole locations after quantization, one has to derive structures where the coefficients of the multipliers are given by other values than the direct form coefficients $a_1$ and $a_2$. \n", "\n", "One of these alternative structures is the coupled form (also known as Gold & Rader structure)\n", "\n", "![Coupled form second order section](coupled_form.png)\n", "\n", "where $\\Re\\{z_\\infty\\} = r \\cdot \\cos \\varphi$ and $\\Im\\{z_\\infty\\} = r \\cdot \\sin \\varphi$ denote the real- and imaginary part of the complex pole $z_\\infty$, respectively. Analysis of the structure reveals its difference equation as\n", "\n", "\\begin{align}\n", "w[k] &= x[k] + \\Re\\{z_\\infty\\} \\, w[k-1] - \\Im\\{z_\\infty\\} \\, y[k-1] \\\\\n", "y[k] &= \\Im\\{z_\\infty\\} \\, w[k-1] + \\Re\\{z_\\infty\\} \\, y[k-1]\n", "\\end{align}\n", "\n", "and its transfer function as\n", "\n", "\\begin{equation}\n", "H(z) = \\frac{\\Im\\{z_\\infty\\} \\; z^{-1}}{ 1 - 2 \\Re\\{z_\\infty\\} \\; z^{-1} + (\\Re\\{z_\\infty\\}^2 + \\Im\\{z_\\infty\\}^2) \\; z^{-2} }\n", "\\end{equation}\n", "\n", "Note that the numerator of the transfer function differs from the recursive only SOS given above. However, this can be considered in the design of the transfer function of a general SOS.\n", "\n", "The real- and imaginary part of the pole $z_\\infty$ occur directly as coefficients for the multipliers in the coupled form. Quantization of these coefficients results therefore in a Cartesian grid of possible pole locations in the $z$-plane. This is illustrated in the following." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def compute_pole_locations(w):\n", " Q = 1/(2**(w-1)) # quantization stepsize\n", " a1 = np.arange(-1, 1+Q, Q)\n", " a2 = np.arange(-1, 1+Q, Q)\n", " \n", " p = np.asarray([n+1j*m for (n,m) in itertools.product(a1, a2) if n**2+m**2 <= 1])\n", "\n", " return p\n", "\n", "def plot_pole_locations(p):\n", " ax = plt.gca()\n", " \n", " unit_circle = Circle((0,0), radius=1, fill=False, color='red', ls='solid')\n", " ax.add_patch(unit_circle) \n", "\n", " plt.plot(np.real(p), np.imag(p), 'b.', ms = 4)\n", " plt.xlabel(r'Re{$z$}')\n", " plt.ylabel(r'Im{$z$}')\n", " plt.axis([-1.1, 1.1, -1.1, 1.1])\n", "\n", " \n", "# compute and plot pole locations\n", "for w in [5,6]:\n", " plt.figure(figsize=(5, 5))\n", " p = compute_pole_locations(w)\n", " plot_pole_locations(p)\n", " plt.title(r'Coupled form coefficient quantization to $w=%d$ bits'%w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Excercise**\n", "\n", "* What is the benefit of this representation in comparison to the direct from discussed in the previous section?\n", "\n", "Solution: A befit of the coupled form is a uniform distribution of potential pole and zero locations in the $z$-plane. This holds especially for low frequencies and close to the Nyquist frequency." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example - Influence of coefficient quantization\n", "\n", "The following example illustrates the effects of coefficient quantization for a recursive [Butterworth filter](https://en.wikipedia.org/wiki/Butterworth_filter) realized in cascaded SOSs in transposed direct form II." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "w = 16 # wordlength of filter coefficients\n", "N = 7 # order of filter\n", "\n", "\n", "def uniform_midtread_quantizer(x, w, xmin=1):\n", " # quantization step\n", " Q = xmin/(2**(w-1))\n", " # limiter\n", " x = np.copy(x)\n", " idx = np.where(x <= -xmin)\n", " x[idx] = -1\n", " idx = np.where(x > xmin - Q)\n", " x[idx] = 1 - Q\n", " # linear uniform quantization\n", " xQ = Q * np.floor(x/Q + 1/2)\n", " \n", " return xQ\n", "\n", "\n", "def zplane(z, p, title='Poles and Zeros'):\n", " \"Plots zero and pole locations in the complex z-plane\"\n", " ax = plt.gca()\n", " \n", " ax.plot(np.real(z), np.imag(z), 'bo', fillstyle='none', ms = 10)\n", " ax.plot(np.real(p), np.imag(p), 'rx', fillstyle='none', ms = 10)\n", " unit_circle = Circle((0,0), radius=1, fill=False,\n", " color='black', ls='solid', alpha=0.9)\n", " ax.add_patch(unit_circle)\n", " ax.axvline(0, color='0.7')\n", " ax.axhline(0, color='0.7')\n", " \n", " plt.title(title)\n", " plt.xlabel(r'Re{$z$}')\n", " plt.ylabel(r'Im{$z$}')\n", " plt.axis('equal')\n", " plt.xlim((-2, 2))\n", " plt.ylim((-2, 2))\n", " plt.grid()\n", "\n", " \n", "# coefficients of recursive filter\n", "b, a = sig.butter(N, 0.2, 'low')\n", "# decomposition into SOS\n", "sos = sig.tf2sos(b, a, pairing='nearest')\n", "sos = sos/np.amax(np.abs(sos))\n", "# quantization of SOS coefficients\n", "sosq = uniform_midtread_quantizer(sos, w, xmin=1)\n", "# compute overall transfer function of (quantized) filter\n", "H = np.ones(512)\n", "Hq = np.ones(512)\n", "for n in range(sos.shape[0]):\n", " Om, Hn = sig.freqz(sos[n, 0:3], sos[n, 3:6])\n", " H = H * Hn\n", " Om, Hn = sig.freqz(sosq[n, 0:3], sosq[n, 3:6])\n", " Hq = Hq * Hn\n", "\n", "\n", "# plot magnitude responses\n", "plt.figure(figsize=(10, 3))\n", "plt.plot(Om, 20 * np.log10(abs(H)), label='continuous')\n", "plt.plot(Om, 20 * np.log10(abs(Hq)), label='quantized')\n", "plt.title('Magnitude response')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$|H(e^{j \\Omega})|$ in dB')\n", "plt.legend(loc=3)\n", "plt.grid()\n", "# plot phase responses\n", "plt.figure(figsize=(10, 3))\n", "plt.plot(Om, np.unwrap(np.angle(H)), label='continuous')\n", "plt.plot(Om, np.unwrap(np.angle(Hq)), label='quantized')\n", "plt.title('Phase')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$\\varphi (\\Omega)$ in rad')\n", "plt.legend(loc=3)\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Decrease the word length `w` of the filter. What happens? At what word length does the filter become unstable?\n", "* Increase the order `N` of the filter for a fixed word length `w`. What happens?\n", "\n", "Solution: The deviations from the continuous (desired) realization of the filter increase with decreasing word length. The filter with order `N=5` becomes unstable for `w < 10`. Increasing the order `N` of the filter for a fixed word length results also in instabilities. Consequently, for a high order filter also a higher word length is required." ] }, { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "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, 2016-2018*." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 1 }