{ "cells": [ { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "# Design of Digital 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": [ "## Design of Non-Recursive Filters using the Window Method\n", "\n", "The design of non-recursive filters with a finite-length impulse response (FIR) is a frequent task in practical applications. The designed filter should approximate a prescribed frequency response as close as possible. First, the design of causal filters is considered. For many applications the resulting filter should have a linear phase characteristic since this results in a constant (frequency independent) group delay. We therefore specialize the design to causal linear-phase filters in a second step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Causal Filters\n", "\n", "Let's assume that the desired frequency characteristic of the discrete filter is given by its continuous frequency response $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ in the discrete-time Fourier domain. Its impulse response is given by inverse discrete-time Fourier transform (inverse DTFT) of the frequency response\n", "\n", "\\begin{equation}\n", "h_\\text{d}[k] = \\frac{1}{2 \\pi} \\int\\limits_{- \\pi}^{\\pi} H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\, \\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega\\,k} \\; \\mathrm{d}\\Omega\n", "\\end{equation}\n", "\n", "In the general case, $h_\\text{d}[k]$ will not be a causal FIR. The [Paley-Wiener theorem](https://en.wikipedia.org/wiki/Paley%E2%80%93Wiener_theorem) states, that the transfer function of a causal system may only have zeros at a countable number of single frequencies. This is not the case for idealized filters, like e.g. the [ideal low-pass filter](https://en.wikipedia.org/wiki/Low-pass_filter#Ideal_and_real_filters), were the transfer function is zeros over an interval of frequencies. The basic idea of the window method is to truncate the impulse response $h_\\text{d}[k]$ in order to derive a causal FIR filter. This can be achieved by applying a window $w[k]$ of finite length $N$ to $h_\\text{d}[k]$\n", "\n", "\\begin{equation}\n", "h[k] = h_\\text{d}[k] \\cdot w[k]\n", "\\end{equation}\n", "\n", "where $h[k]$ denotes the impulse response of the designed filter and $w[k] = 0$ for $\\{k : k < 0 \\vee k \\geq N\\}$. Its frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is given by the multiplication theorem of the discrete-time Fourier transform (DTFT)\n", "\n", "\\begin{equation}\n", "H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{1}{2 \\pi} \\; H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\circledast W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\n", "\\end{equation}\n", "\n", "where $W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ denotes the DTFT of the window function $w[k]$. The frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ of the filter is given as the periodic convolution of the desired frequency response $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and the frequency response of the window function $W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. The frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is equal to the desired frequency response $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ only if $W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = 2 \\pi \\cdot \\delta(\\Omega)$. This would require that $w[k] = 1$ for $k = -\\infty, \\dots, \\infty$. Hence for a window $w[k]$ of finite length, deviations from the desired frequency response are to be expected.\n", "\n", "In order to investigate the effect of truncation on the frequency response $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$, a particular window is considered. A straightforward choice is the rectangular window $w[k] = \\text{rect}_N[k]$ of length $N$. Its DTFT is given as\n", "\n", "\\begin{equation}\n", "W(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\mathrm{e}^{-\\mathrm{j} \\, \\Omega \\,\\frac{N-1}{2}} \\cdot \\frac{\\sin(\\frac{N \\,\\Omega}{2})}{\\sin(\\frac{\\Omega}{2})}\n", "\\end{equation}\n", "\n", "The frequency-domain properties of the rectangular window have already been discussed for the [leakage effect](../spectral_analysis_deterministic_signals/leakage_effect.ipynb). The rectangular window features a narrow main lobe at the cost of relative high sidelobe level. The main lobe gets narrower with increasing length $N$. The convolution of the desired frequency response with the frequency response of the window function effectively results in smoothing and ringing. While the main lobe will smooth discontinuities of the desired transfer function, the sidelobes result in undesirable ringing effects. The latter can be alleviated by using other window functions. Note that typical [window functions](../spectral_analysis_deterministic_signals/window_functions.ipynb) decay towards their ends and are symmetric with respect to their center. This may cause problems for desired impulse responses with large magnitudes towards their ends." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example - Causal approximation of ideal low-pass\n", "\n", "The design of an ideal low-pass filter using the window method is illustrated in the following. For $|\\Omega| < \\pi$ the transfer function of the ideal low-pass is given as\n", "\n", "\\begin{equation}\n", "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\begin{cases}\n", "1 & \\text{for } |\\Omega| \\leq \\Omega_\\text{c} \\\\\n", "0 & \\text{otherwise}\n", "\\end{cases}\n", "\\end{equation}\n", "\n", "where $\\Omega_\\text{c}$ denotes the cut frequency of the low-pass. An inverse DTFT of the desired transfer function yields\n", "\n", "\\begin{equation}\n", "h_\\text{d}[k] = \\frac{\\Omega_\\text{c}}{\\pi} \\cdot \\text{sinc}(\\Omega_\\text{c} \\, k)\n", "\\end{equation}\n", "\n", "The impulse response $h_\\text{d}[k]$ is not causal nor FIR. In order to derive a causal FIR approximation, a rectangular window $w[k]$ of length $N$ is applied\n", "\n", "\\begin{equation}\n", "h[k] = h_\\text{d}[k] \\cdot \\text{rect}_N[k]\n", "\\end{equation}\n", "\n", "The resulting magnitude and phase response is computed numerically in the following." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.signal as sig\n", "\n", "%matplotlib inline\n", "\n", "N = 32 # length of filter\n", "Omc = np.pi / 2\n", "\n", "# compute impulse response\n", "k = np.arange(N)\n", "hd = Omc / np.pi * np.sinc(k * Omc / np.pi)\n", "# windowing\n", "w = np.ones(N)\n", "h = hd * w\n", "\n", "# frequency response\n", "Om, H = sig.freqz(h)\n", "\n", "# plot impulse response\n", "plt.figure(figsize=(10, 3))\n", "plt.stem(h)\n", "plt.title(\"Impulse response\")\n", "plt.xlabel(r\"$k$\")\n", "plt.ylabel(r\"$h[k]$\")\n", "# plot magnitude responses\n", "plt.figure(figsize=(10, 3))\n", "plt.plot([0, Omc, Omc], [0, 0, -100], \"r--\", label=\"desired\")\n", "plt.plot(Om, 20 * np.log10(abs(H)), label=\"window method\")\n", "plt.title(\"Magnitude response\")\n", "plt.xlabel(r\"$\\Omega$\")\n", "plt.ylabel(r\"$|H(e^{j \\Omega})|$ in dB\")\n", "plt.axis([0, np.pi, -20, 3])\n", "plt.grid()\n", "plt.legend()\n", "# plot phase responses\n", "plt.figure(figsize=(10, 3))\n", "plt.plot([0, Om[-1]], [0, 0], \"r--\", label=\"desired\")\n", "plt.plot(Om, np.unwrap(np.angle(H)), label=\"window method\")\n", "plt.title(\"Phase\")\n", "plt.xlabel(r\"$\\Omega$\")\n", "plt.ylabel(r\"$\\varphi (\\Omega)$ in rad\")\n", "plt.grid()\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercises**\n", "\n", "* Does the resulting filter have the desired phase?\n", "* Increase the length `N` of the filter. What changes?\n", "\n", "Solution: The desired filter has zero-phase for all frequencies, hence $\\varphi_\\text{d}(\\Omega) = 0$. The phase of the resulting filter is not zero as can be concluded from the lower illustration. The small local variations (ripples) in the magnitude $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ of the transfer function of the resulting filter decrease with an increasing number `N` of filter coefficients. The achievable attenuation in the stop-band of the low-pass does not change." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Zero-Phase Filters\n", "\n", "Lets assume a general zero-phase filter with transfer function $H_d(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ with magnitude $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\in \\mathbb{R}$. Due to the symmetry relations of the DTFT, its impulse response $h_d[k] = \\mathcal{F}_*^{-1} \\{ H_d(e^{j \\Omega} \\}$ is conjugate complex symmetric\n", "\n", "\\begin{equation}\n", "h_d[k] = h_d^*[-k]\n", "\\end{equation}\n", "\n", "A zero-phase filter of length $N > 1$ is not causal as a consequence. The anti-causal part could simply be removed by windowing with a heaviside signal. However, this will result in large deviations between the desired transfer function and the designed filter. This explains the findings from the previous example, that an ideal-low pass cannot be realized very well by the window method. The reason is that an ideal-low pass has zero-phase, as most of the idealized filters.\n", "\n", "The impulse response of a stable system, in the sense of the bounded-input/bounded-output (BIBO) criterion, has to be absolutely summable. Which in general is given when its magnitude decays by tendency with increasing time-index $k$.\n", "This observation motivates to shift the desired impulse response to the center of the window in order to limit the effect of windowing. This can be achieved by replacing the zero-phase with a linear-phase, as is illustrated below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Causal Linear-Phase Filters\n", "\n", "The design of a non-recursive causal FIR filter with a linear phase is often desired due to its constant group delay. Let's assume a filter with generalized linear phase. For $|\\Omega| < \\pi$ its transfer function is given as\n", "\n", "\\begin{equation}\n", "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\cdot \\mathrm{e}^{-\\mathrm{j} \\alpha \\Omega + \\mathrm{j} \\beta}\n", "\\end{equation}\n", "\n", "where $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\in \\mathbb{R}$ denotes the amplitude of the filter, $\\alpha$ the linear slope of the phase and $\\beta$ a constant phase offset. Such a system can be decomposed into two cascaded systems: a zero-phase system with transfer function $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and an all-pass with phase $\\varphi(\\Omega) = - \\alpha \\Omega + \\beta$. The linear phase term $- \\alpha \\Omega$ results in the constant group delay $t_g(\\Omega) = \\alpha$. \n", "\n", "The impulse response $h[k]$ of a linear-phase system shows a specific symmetry which can be deduced from the symmetry relations of the DTFT for odd/even symmetry of $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ as\n", "\n", "\\begin{equation}\n", "h[k] = \\pm h[N-1-k]\n", "\\end{equation}\n", "\n", "for $k=0, 1, \\dots, N-1$ where $N \\in \\mathbb{N}$ denotes the length of the (finite) impulse response. The transfer function of a linear phase filter is given by its DTFT\n", "\n", "\\begin{equation}\n", "H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\sum_{k=0}^{N-1} h[k] \\, \\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega\\,k}\n", "\\end{equation}\n", "\n", "Introducing the symmetry relations of the impulse response $h[k]$ into the DTFT and comparing the result with above definition of a generalized linear phase system reveals four different types of linear-phase systems. These can be discriminated with respect to their phase and magnitude characteristics\n", "\n", "| Type | Length $N$ | Impulse Response $h[k]\\;$ | Group Delay $\\alpha$ in Samples| Constant Phase $\\beta$ | Transfer Function $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ |\n", "| :---: | :---: | :---: | :---:| :---: | :---: |\n", "| 1 | odd | $h[k] = h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\in \\mathbb{N}$ | $\\beta = \\{0, \\pi\\}$ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})=A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, all filter characteristics|\n", "| 2 | even| $h[k] = h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\notin \\mathbb{N}$ | $\\beta = \\{0, \\pi\\}$ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})=A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\pi}) = 0$, only lowpass or bandpass|\n", "| 3 | odd | $h[k] = -h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\in \\mathbb{N}$ | $\\beta = \\{ \\frac{\\pi}{2}, \\frac{3 \\pi}{2} \\}$ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})=-A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, $A(\\mathrm{e}^{\\,\\mathrm{j}\\,0}) = A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\pi}) = 0$, only bandpass|\n", "| 4 | even | $h[k] = -h[N-1-k]$ | $\\alpha = \\frac{N-1}{2} \\notin \\mathbb{N}$ | $\\beta = \\{ \\frac{\\pi}{2}, \\frac{3 \\pi}{2} \\}$ | $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})=-A(\\mathrm{e}^{-\\,\\mathrm{j}\\,\\Omega})$, $A(\\mathrm{e}^{\\,\\mathrm{j}\\,0}) = 0$, only highpass or bandpass|\n", "\n", "These relations have to be considered in the design of a causal linear phase filter. Depending on the desired magnitude characteristics $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ the suitable type is chosen. The odd/even length $N$ of the filter and the phase (or group delay) is chosen accordingly for the design of the filter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example - Causal linear-phase approximation of ideal low-pass\n", "\n", "We aim at the design of a causal linear-phase low-pass using the window technique. According to the previous example, the desired frequency response has an even symmetry $A(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = A(\\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega})$ with $A(\\mathrm{e}^{\\mathrm{j}\\,0}) = 1$. This could be realized by a filter of type 1 or 2. We choose type 1 with $\\beta = 0$, since the resulting filter exhibits an integer group delay of $t_g(\\Omega) = \\frac{N-1}{2}$ samples. Consequently the length of the filter $N$ has to be odd. \n", "\n", "The impulse response $h_\\text{d}[k]$ is given by the inverse DTFT of $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ incorporating the linear phase\n", "\n", "\\begin{equation}\n", "h_\\text{d}[k] = \\frac{\\Omega_\\text{c}}{\\pi} \\cdot \\text{sinc} \\left( \\Omega_\\text{c} \\left(k-\\frac{N-1}{2} \\right) \\right)\n", "\\end{equation}\n", "\n", "The impulse response fulfills the desired symmetry for $k=0,1, \\dots, N-1$. A causal FIR approximation is obtained by applying a window function of length $N$ to the impulse response $h_\\text{d}[k]$\n", "\n", "\\begin{equation}\n", "h[k] = h_\\text{d}[k] \\cdot w[k]\n", "\\end{equation}\n", "\n", "Note that the window function $w[k]$ also has to fulfill the desired symmetries.\n", "\n", "As already outlined, the chosen window determines the properties of the transfer function $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. The [spectral properties of commonly applied windows](../spectral_analysis_deterministic_signals/window_functions.ipynb) have been discussed previously. The width of the main lobe will generally influence the smoothing of the desired transfer function $H_\\text{d}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$, while the sidelobes influence the typical ringing artifacts. This is illustrated in the following." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 33 # length of filter\n", "Omc = np.pi / 2\n", "\n", "# compute impulse response\n", "k = np.arange(N)\n", "hd = Omc / np.pi * np.sinc((k - (N - 1) / 2) * Omc / np.pi)\n", "# windowing\n", "w1 = np.ones(N)\n", "w2 = np.blackman(N)\n", "h1 = hd * w1\n", "h2 = hd * w2\n", "\n", "# frequency responses\n", "Om, H1 = sig.freqz(h1)\n", "Om, H2 = sig.freqz(h2)\n", "\n", "# plot impulse response\n", "plt.figure(figsize=(10, 3))\n", "plt.stem(h1)\n", "plt.title(\"Impulse response (rectangular window)\")\n", "plt.xlabel(r\"$k$\")\n", "plt.ylabel(r\"$h[k]$\")\n", "# plot magnitude responses\n", "plt.figure(figsize=(10, 3))\n", "plt.plot([0, Omc, Omc], [0, 0, -300], \"r--\", label=\"desired\")\n", "plt.plot(Om, 20 * np.log10(abs(H1)), label=\"rectangular window\")\n", "plt.plot(Om, 20 * np.log10(abs(H2)), label=\"Blackmann window\")\n", "plt.title(\"Magnitude response\")\n", "plt.xlabel(r\"$\\Omega$\")\n", "plt.ylabel(r\"$|H(e^{j \\Omega})|$ in dB\")\n", "plt.axis([0, np.pi, -120, 3])\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(H1)), label=\"rectangular window\")\n", "plt.plot(Om, np.unwrap(np.angle(H2)), label=\"Blackmann window\")\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": [ "**Exercises**\n", "\n", "* Does the impulse response fulfill the required symmetries for a type 1 filter?\n", "* Can you explain the differences between the magnitude responses $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ for the different window functions?\n", "* What happens if you increase the length `N` of the filter?\n", "\n", "Solution: Inspection of the impulse response reveals that it shows the symmetry $h[k] = h[N-1-k]$ of a type 1 filter for odd `N`. The rectangular window features a narrow main lobe at the cost of a high level of the side lobes, the main lobe of the Blackmann window is wider but the level of the side lobes is lower compared to the rectangular window. This explains the behavior of the magnitude responses $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ in the stop-band of the realized low-passes. The distance between the local minima in the magnitude responses $|H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|$ decreases with increasing length `N` and the attenuation for frequencies towards the Nyquist frequency increases." ] }, { "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*." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.6" } }, "nbformat": 4, "nbformat_minor": 4 }