{ "cells": [ { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "# Random Signals and LTI-Systems\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": [ "## The Wiener Filter\n", "\n", "The [Wiener filter](https://en.wikipedia.org/wiki/Wiener_filter), named after [*Nobert Wiener*](https://en.wikipedia.org/wiki/Norbert_Wiener), aims at estimating an unknown random signal by filtering a noisy distorted observation of the signal. It has a wide range of applications in signal processing. For instance, noise reduction, system identification, deconvolution and signal detection. The Wiener filter is frequently used as basic building block for algorithms that denoise audio signals, like speech, or remove noise from a image." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Signal Model\n", "\n", "The following signal model is underlying the Wiener filter\n", "\n", "![Illustration: Signal model for the Wiener filter](model_wiener_filter.png)\n", "\n", "The random signal $s[k]$ is subject to distortion by the linear time-invariant (LTI) system $G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and additive noise $n[k]$, resulting in the observed signal $x[k] = s[k] * g[k] + n[k]$. The additive noise $n[k]$ is assumed to be uncorrelated from $s[k]$. It is furthermore assumed that all random signals are wide-sense stationary (WSS). This distortion model holds for many practical problems, like e.g. the measurement of a physical quantity by a sensor.\n", "\n", "The basic concept of the Wiener filter is to apply the LTI system $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ to the observed signal $x[k]$ such that the output signal $y[k] = x[k] * h[k]$ matches $s[k]$ as close as possible. In order to quantify the deviation between $y[k]$ and $s[k]$, the error signal\n", "\n", "\\begin{equation}\n", "e[k] = y[k] - s[k]\n", "\\end{equation}\n", "\n", "is introduced. The error $e[k]$ equals zero, if the output signal $y[k]$ perfectly matches $s[k]$. In general, this goal cannot be achieved in a strict sense. As alternative one could aim at minimizing the linear average of the error $e[k]$. However, this quantity is not very well suited for optimization since it is signed. Instead, the quadratic average of the error $e[k]$ is used in the Wiener filter and other techniques. This measure is known as [*mean squared error*](https://en.wikipedia.org/wiki/Mean_squared_error) (MSE). It is defined as\n", "\n", "\\begin{equation}\n", "E \\{ |e[k]|^2 \\} = \\frac{1}{2 \\pi} \\int\\limits_{-\\pi}^{\\pi} \\Phi_{ee}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\,\\mathrm{d}\\Omega = \\varphi_{ee}[\\kappa] \\Big\\vert_{\\kappa = 0}\n", "\\end{equation}\n", "\n", "the equalities are deduced from the properties of the power spectral density (PSD) and the auto-correlation function (ACF). Above equation is referred to as [*cost function*](https://en.wikipedia.org/wiki/Loss_function). We aim at minimizing the cost function, hence minimizing the MSE between the original signal $s[k]$ and its estimate $y[k]$. The solution is referred to as [minimum mean squared error](https://en.wikipedia.org/wiki/Minimum_mean_square_error) (MMSE) solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Transfer Function of the Wiener Filter\n", "\n", "At first, the Wiener filter shall only have access to the observed signal $x[k]$ and selected statistical measures. It is assumed that the cross-power spectral density $\\Phi_{xs}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ between the observed signal $x[k]$ and the original signal $s[k]$, and the PSD of the observed signal $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ are known. This knowledge can either be gained by estimating both from measurements taken at an actual system or by using suitable statistical models.\n", "\n", "The optimal filter is found by minimizing the MSE $E \\{ |e[k]|^2 \\}$ with respect to the transfer function $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$. The solution of this optimization problem goes beyond the scope of this notebook and can be found in the literature, e.g. [[Girod et. al](../index.ipynb#Literature)]. The transfer function of the Wiener filter is given as\n", "\n", "\\begin{equation}\n", "H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{\\Phi_{sx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}{\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})} = \\frac{\\Phi_{xs}(\\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega})}{\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}\n", "\\end{equation}\n", "\n", "for $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\neq 0$.\n", "No knowledge on the actual distortion process is required besides the assumption of an LTI system and additive noise. Only the PSDs $\\Phi_{sx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ have to be known in order to estimate $s[k]$ from $x[k]$ in the MMSE sense. Care has to be taken that the filter $H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ is causal and stable in practical applications." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Example - Denoising of an Deterministic Signal**\n", "\n", "The following example considers the estimation of the original signal from a distorted observation. It is assumed that the original signal is a deterministic signal $s[k] = \\sin[\\Omega_0\\,k]$ which is distorted by an LTI system and additive wide-sense ergodic normal distributed zero-mean white noise with PSD $N_0 = 0.1$. The PSDs $\\Phi_{sx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ are estimated from $s[k]$ and $x[k]$ using the [Welch technique](../spectral_estimation_random_signals/welch_method.ipynb). The Wiener filter is applied to the observation $x[k]$ in order to compute the estimate $y[k]$ of $s[k]$. Note that the discrete signals have been illustrated by continuous lines for ease of illustration." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n"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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.signal as sig\n", "\n", "N = 8129 # number of samples\n", "M = 256 # length of Wiener filter\n", "Om0 = 0.1*np.pi # frequency of original signal\n", "N0 = 0.1 # PSD of additive white noise\n", "\n", "# generate original signal\n", "s = np.cos(Om0 * np.arange(N)) \n", "# generate observed signal\n", "g = 1/20*np.asarray([1, 2, 3, 4, 5, 4, 3, 2, 1])\n", "np.random.seed(1)\n", "n = np.random.normal(size=N, scale=np.sqrt(N0))\n", "x = np.convolve(s, g, mode='same') + n\n", "# estimate (cross) PSDs using Welch technique\n", "f, Pxx = sig.csd(x, x, nperseg=M)\n", "f, Psx = sig.csd(s, x, nperseg=M)\n", "# compute Wiener filter\n", "H = Psx/Pxx\n", "H = H * np.exp(-1j*2*np.pi/len(H)*np.arange(len(H))*(len(H)//2)) # shift for causal filter\n", "h = np.fft.irfft(H)\n", "# apply Wiener filter to observation\n", "y = np.convolve(x, h, mode='same')\n", "\n", "# plot (cross) PSDs\n", "Om = np.linspace(0, np.pi, num=len(H))\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(121)\n", "plt.plot(Om, 20*np.log10(np.abs(.5*Pxx)), label=r'$| \\Phi_{xx}(e^{j \\Omega}) |$ in dB')\n", "plt.plot(Om, 20*np.log10(np.abs(.5*Psx)), label=r'$| \\Phi_{sx}(e^{j \\Omega}) |$ in dB')\n", "plt.title('(Cross) PSDs')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.legend()\n", "plt.axis([0, np.pi, -60, 40])\n", "plt.grid()\n", "\n", "# plot transfer function of Wiener filter\n", "plt.subplot(122)\n", "plt.plot(Om, 20*np.log10(np.abs(H)))\n", "plt.title('Transfer function of Wiener filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$| H(e^{j \\Omega}) |$ in dB')\n", "plt.axis([0, np.pi, -150, 3])\n", "plt.grid()\n", "plt.tight_layout()\n", "\n", "# plot signals\n", "idx = np.arange(500, 600)\n", "plt.figure(figsize=(10, 4))\n", "plt.plot(idx, x[idx], label=r'observed signal $x[k]$')\n", "plt.plot(idx, s[idx], label=r'original signal $s[k]$')\n", "plt.plot(idx, y[idx], label=r'estimated signal $y[k]$')\n", "plt.title('Signals')\n", "plt.xlabel(r'$k$')\n", "plt.axis([idx[0], idx[-1], -1.5, 1.5])\n", "plt.legend()\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Take a look at the PSDs and the resulting transfer function of the Wiener filter. How does the Wiener filter remove the noise from the observed signal?\n", "* Change the frequency `Om0` of the original signal $s[k]$ and the noise power `N0` of the additive noise. What changes?\n", "\n", "Solution: The cross-PSD $\\Phi_{sx}(e^{j \\Omega})$ has its maximum at the frequency $\\Omega_0$ of the original signal $s[k]$, besides this frequency the PSD $\\Phi_{xx}(e^{j \\Omega})$ has approximately the value of the PSD $\\Phi_{nn}(e^{j \\Omega}) = N_0$ of the additive noise. The resulting Wiener filter $G(e^{j \\Omega})$ has an attenuation of 0 dB at $\\Omega_0$ which increases off this frequency. It has the characteristics of a band-pass filter centered at $\\Omega_0$. By filtering the observed signal $x[k]$ with the Wiener filter, the major portion of the additive white noise is removed. However, around $\\Omega_0$ both the original signal $s[k]$ and noise pass the filter. This explains the remaining small deviations between the estimated signal $y[k]$ and the original signal $y[k]$. The adaption of the Wiener filter to the original signal and additive noise changes when changing its frequency and PSD." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Wiener Deconvolution\n", "\n", "As discussed above, the general formulation of the Wiener filter is based on the knowledge of the PSDs $\\Phi_{sx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and $\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ characterizing the distortion process and the observed signal, respectively. These PSDs can be derived from the PSDs of the original signal $\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ and the noise $\\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$, and the transfer function $G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ of the distorting system.\n", "\n", "Under the assumption that $n[k]$ is uncorrelated from $s[k]$, the PSD $\\Phi_{sx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ can be derived as\n", "\n", "\\begin{equation}\n", "\\Phi_{sx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\cdot G(\\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega})\n", "\\end{equation}\n", "\n", "and\n", "\n", "\\begin{equation}\n", "\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\cdot |G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|^2 + \\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\n", "\\end{equation}\n", "\n", "Introducing these results into the general formulation of the Wiener filter yields\n", "\n", "\\begin{equation}\n", "H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\cdot G(\\mathrm{e}^{\\,-\\mathrm{j}\\,\\Omega})}{\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) \\cdot |G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|^2 + \\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}\n", "\\end{equation}\n", "\n", "This specialization is also known as [*Wiener deconvolution filter*](https://en.wikipedia.org/wiki/Wiener_deconvolution). The filter can be derived from the PSDs of the original signal $s[k]$ and the noise $n[k]$, and the transfer function $G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ of the distorting system. This form is especially useful when the PSDs can be modeled reasonably well by analytic probabilty density functions (PSDs). In many cases, the additive noise can be modeled as white noise $\\Phi_{nn}(e^{j \\Omega}) = N_0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interpretation\n", "\n", "The Wiener deconvolution filter derived above is also useful for an interpretation of the operation of the Wiener filter. It can be rewritten by introducing the frequency dependent [signal-to-noise ratio](https://en.wikipedia.org/wiki/Signal-to-noise_ratio) $\\text{SNR}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}{\\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}$ between the original signal and the noise as\n", "\n", "\\begin{equation}\n", "H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{1}{G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})} \\cdot \\left( \\frac{|G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|^2}{|G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})|^2 + \\frac{1}{\\text{SNR}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}} \\right)\n", "\\end{equation}\n", "\n", "Now two special cases are discussed:\n", "\n", "1. If there is no additive noise $\\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = 0$, the bracketed expression is equal to 1. Hence, the Wiener filter is simply given as the inverse system to the distorting system $$H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{1}{G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}$$\n", "\n", "2. If the distorting system is just a pass-through $G(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = 1$, the Wiener filter is given as\n", "\n", " $$H(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\frac{\\text{SNR}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}{\\text{SNR}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) + 1}=\\frac{\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}{\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})+\\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})}$$\n", " Two extreme cases are considered\n", " * for $\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\\gg \\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ (high $\\text{SNR}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$) at a given frequency $\\Omega$ the transfer function approaches 1\n", " * for $\\Phi_{ss}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})\\ll \\Phi_{nn}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$ (low $\\text{SNR}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega})$) at a given frequency $\\Omega$ the transfer function approaches 0\n", " \n", "The discussed cases explain the operation of the Wiener filter for specific situations, the general operation is a combination of these." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Example - Denoising of a deterministic signal with the Wiener deconvolution filter**\n", "\n", "The preceding example of the general Wiener filter will now be reevaluated with the Wiener deconvolution filter." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 8129 # number of samples\n", "M = 256 # length of Wiener filter\n", "Om0 = 0.1*np.pi # frequency of original signal\n", "N0 = .1 # PSD of additive white noise\n", "\n", "# generate original signal\n", "s = np.cos(Om0 * np.arange(N)) \n", "# generate observed signal\n", "g = 1/20*np.asarray([1, 2, 3, 4, 5, 4, 3, 2, 1])\n", "np.random.seed(1)\n", "n = np.random.normal(size=N, scale=np.sqrt(N0))\n", "x = np.convolve(s, g, mode='same') + n\n", "# estimate PSD\n", "f, Pss = sig.csd(s, s, nperseg=M)\n", "f, Pnn = sig.csd(n, n, nperseg=M)\n", "# compute Wiener filter\n", "G = np.fft.rfft(g, M)\n", "H = 1/G * (np.abs(G)**2 / (np.abs(G)**2 + N0/Pss))\n", "H = H * np.exp(-1j*2*np.pi/len(H)*np.arange(len(H))*(len(H)//2-8)) # shift for causal filter\n", "h = np.fft.irfft(H)\n", "# apply Wiener filter to observation\n", "y = np.convolve(x, h, mode='same')\n", "\n", "# plot (cross) PSDs\n", "Om = np.linspace(0, np.pi, num=len(H))\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(121)\n", "plt.plot(Om, 20*np.log10(np.abs(.5*Pss)), label=r'$| \\Phi_{ss}(e^{j \\Omega}) |$ in dB')\n", "plt.plot(Om, 20*np.log10(np.abs(.5*Pnn)), label=r'$| \\Phi_{nn}(e^{j \\Omega}) |$ in dB')\n", "plt.title('PSDs')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.legend()\n", "plt.axis([0, np.pi, -60, 40])\n", "plt.grid()\n", "\n", "# plot transfer function of Wiener filter\n", "plt.subplot(122)\n", "plt.plot(Om, 20*np.log10(np.abs(H)))\n", "plt.title('Transfer function of Wiener filter')\n", "plt.xlabel(r'$\\Omega$')\n", "plt.ylabel(r'$| H(e^{j \\Omega}) |$ in dB')\n", "plt.axis([0, np.pi, -150, 10])\n", "plt.grid()\n", "plt.tight_layout()\n", "\n", "# plot signals\n", "idx = np.arange(500, 600)\n", "plt.figure(figsize=(10, 4))\n", "plt.plot(idx, x[idx], label=r'observed signal $x[k]$')\n", "plt.plot(idx, s[idx], label=r'original signal $s[k]$')\n", "plt.plot(idx, y[idx], label=r'estimated signal $y[k]$')\n", "plt.title('Signals')\n", "plt.xlabel(r'$k$')\n", "plt.axis([idx[0], idx[-1], -1.5, 1.5])\n", "plt.legend()\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Compare the transfer function of the Wiener deconvolution filter to the transfer function of the general Wiener filter from the preceding example.\n", "* What is different compared to the general Wiener filter? Why?\n", "\n", "Solution: The transfer function $H(e^{j \\Omega})$ of the Wiener deconvolution filter is much smoother than the transfer function of the general Wiener filter from the preceding example. This is due to the knowledge of the transfer function $G(e^{j \\Omega})$ of the disturbing system. The general Wiener filter inherently estimates this from the noisy observations." ] }, { "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": { "anaconda-cloud": {}, "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 }