{ "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": [ "## Cascaded Structures\n", "\n", "The realization of recursive filters with a high order may be subject to numerical issues. For instance, when the coefficients span a wide amplitude range, their quantization may require a small quantization step or may impose a large relative error for small coefficients. The basic concept of cascaded structures is to decompose a high order filter into a cascade of lower order filters, typically first and second order recursive filters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Decomposition into Second-Order Sections\n", "\n", "The rational transfer function $H(z)$ of a linear time-invariant (LTI) recursive system can be [expressed by its zeros and poles](introduction.ipynb#Transfer-Function) as\n", "\n", "\\begin{equation}\n", "H(z) = \\frac{b_M}{a_N} \\cdot \\frac{\\prod_{\\mu=1}^{P} (z - z_{0\\mu})^{m_\\mu}}{\\prod_{\\nu=1}^{Q} (z - z_{\\infty\\nu})^{n_\\nu}}\n", "\\end{equation}\n", "\n", "where $z_{0\\mu}$ and $z_{\\infty\\nu}$ denote the $\\mu$-th zero and $\\nu$-th pole of degree $m_\\mu$ and $n_\\nu$ of $H(z)$, respectively. The total number of zeros and poles is denoted by $P$ and $Q$.\n", "\n", "The poles and zeros of a real-valued filter $h[k] \\in \\mathbb{R}$ are either single real valued or conjugate complex pairs. This motivates to split the transfer function into\n", "\n", "* first order filters constructed from a single pole and zero\n", "* second order filters constructed from a pair of conjugated complex poles and zeros\n", "\n", "Decomposing the transfer function into these two types by grouping the poles and zeros into single poles/zeros and conjugate complex pairs of poles/zeros results in\n", "\n", "\\begin{equation}\n", "H(z) = K \\cdot \\prod_{\\eta=1}^{S_1} \\frac{(z - z_{0\\eta})}{(z - z_{\\infty\\eta})} \n", "\\cdot \\prod_{\\eta=1}^{S_2} \\frac{(z - z_{0\\eta}) (z - z_{0\\eta}^*)} {(z - z_{\\infty\\eta})(z - z_{\\infty\\eta}^*)}\n", "\\end{equation}\n", "\n", "where $K$ denotes a constant and $S_1 + 2 S_2 = N$ with $N$ denoting the order of the system. The cascade of two systems results in a multiplication of their transfer functions. Above decomposition represents a cascade of first- and second-order recursive systems. The former can be treated as a special case of second-order recursive systems. The decomposition is therefore known as decomposition into second-order sections (SOSs) or [biquad filters](https://en.wikipedia.org/wiki/Digital_biquad_filter). Using a cascade of SOSs the transfer function of the recursive system can be rewritten as\n", "\n", "\\begin{equation}\n", "H(z) = \\prod_{\\mu=1}^{S} \\frac{b_{0, \\mu} + b_{1, \\mu} \\, z^{-1} + b_{2, \\mu} \\, z^{-2}}{1 + a_{1, \\mu} \\, z^{-1} + a_{2, \\mu} \\, z^{-2}}\n", "\\end{equation}\n", "\n", "where $S = \\lceil \\frac{N}{2} \\rceil$ denotes the total number of SOSs. These results state that any real valued system of order $N > 2$ can be decomposed into SOSs. This has a number of benefits\n", "\n", "* quantization effects can be reduced by sensible grouping of poles/zeros, e.g. such that the spanned amplitude range of the filter coefficients is limited\n", "* A SOS may be extended by a gain factor to further reduce quantization effects by normalization of the coefficients\n", "* efficient and numerically stable SOSs serve as generic building blocks for higher-order recursive filters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example - Cascaded second-order section realization of a lowpass\n", "\n", "The following example illustrates the decomposition of a higher-order recursive Butterworth lowpass filter into a cascade of second-order sections." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coefficients of the recursive part \n", "\n", "['1.00', '-5.39', '13.38', '-19.96', '19.62', '-13.14', '5.97', '-1.78', '0.31', '-0.02']\n", "\n", "\n", "Coefficients of the recursive part of the individual SOS \n", "\n", "Section \t a1 \t\t a2\n", "0 \t\t -0.50953 \t 0.00000\n", "1 \t\t -1.04232 \t 0.28838\n", "2 \t\t -1.11568 \t 0.37905\n", "3 \t\t -1.25052 \t 0.54572\n", "4 \t\t -1.46818 \t 0.81477\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "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.markers import MarkerStyle\n", "from matplotlib.patches import Circle\n", "import scipy.signal as sig\n", "\n", "N = 9 # order of recursive filter\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", "# design filter\n", "b, a = sig.butter(N, 0.2)\n", "# decomposition into SOS\n", "sos = sig.tf2sos(b, a, pairing='nearest')\n", "\n", "\n", "# print filter coefficients\n", "print('Coefficients of the recursive part \\n')\n", "print(['%1.2f'%ai for ai in a])\n", "print('\\n')\n", "print('Coefficients of the recursive part of the individual SOS \\n')\n", "print('Section \\t a1 \\t\\t a2')\n", "for n in range(sos.shape[0]):\n", " print('%d \\t\\t %1.5f \\t %1.5f'%(n, sos[n, 4], sos[n, 5]))\n", "\n", "# plot pole and zero locations\n", "plt.figure(figsize=(5,5))\n", "zplane(np.roots(b), np.roots(a), 'Poles and Zeros - Overall')\n", "\n", "plt.figure(figsize=(10, 7))\n", "for n in range(sos.shape[0]): \n", " plt.subplot(231+n)\n", " zplane(np.roots(sos[n, 0:3]), np.roots(sos[n, 3:6]), title='Poles and Zeros - Section %d'%n)\n", "plt.tight_layout()\n", "\n", "# compute and plot frequency response of sections\n", "plt.figure(figsize=(10,5))\n", "for n in range(sos.shape[0]):\n", " Om, H = sig.freqz(sos[n, 0:3], sos[n, 3:6])\n", " plt.plot(Om, 20*np.log10(np.abs(H)), label=r'Section %d'%n)\n", "\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$|H_n(e^{j \\Omega})|$ in dB')\n", "plt.legend()\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* What amplitude range is spanned by the filter coefficients?\n", "* What amplitude range is spanned by the SOS coefficients?\n", "* Change the pole/zero grouping strategy from `pairing='nearest'` to `pairing='keep_odd'`. What changes?\n", "* Increase the order `N` of the filter. What changes?\n", "\n", "Solution: Inspecting both the coefficients of the recursive part of the original filter and of the individual SOS reveals that the spanned amplitude range is lower for the latter. The choice of the pole/zero grouping strategy influences the locations of the poles/zeros in the individual SOS, the spanned amplitude range of their coefficients and the transfer functions of the individual sections. The total number of SOS scales with the order of the original filter." ] }, { "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 }