{ "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": [ "## Introduction\n", "\n", "The response of a system $y[k] = \\mathcal{H} \\{ x[k] \\}$ to a random input signal $x[k]$ is the foundation of statistical signal processing. In the following we limit ourselves to [linear-time invariant (LTI) systems](https://en.wikipedia.org/wiki/LTI_system_theory).\n", "\n", "![LTI system](LTI_system_td.png)\n", "\n", "In the following it is assumed that the statistical properties of the input signal $x[k]$ are known. For instance, its first- and second-order ensemble averages. It is further assumed that the impulse response $h[k]$ or the transfer function $H(e^{\\,\\mathrm{j}\\,\\Omega})$ of the LTI system is given. We are looking for the statistical properties of the output signal $y[k]$ and the joint properties between the input $x[k]$ and output $y[k]$ signal." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stationarity and Ergodicity\n", "\n", "The question arises if the output signal $y[k]$ of an LTI system is (wide-sense) stationary or (wide-sense) ergodic for an input signal $x[k]$ exhibiting the same properties.\n", "\n", "Let's assume that the input signal $x[k]$ is drawn from a stationary random process. According to the [definition of stationarity](../random_signals/stationary_ergodic.ipynb#Definition) the following relation must hold\n", "\n", "\\begin{equation}\n", "E\\{ f(x[k_1], x[k_2], \\dots) \\} = E\\{ f(x[k_1 + \\Delta], x[k_2 + \\Delta], \\dots) \\}\n", "\\end{equation}\n", "\n", "where $\\Delta \\in \\mathbb{Z}$ denotes an arbitrary (temporal) shift and $f(\\cdot)$ an arbitary mapping function. The condition for time-invariance of a system reads\n", "\n", "\\begin{equation}\n", "y[k + \\Delta] = \\mathcal{H} \\{ x[k + \\Delta] \\}\n", "\\end{equation}\n", "\n", "for $y[k] = \\mathcal{H} \\{ x[k] \\}$. Applying the system operator $\\mathcal{H}\\{\\cdot\\}$ to the left- and right-hand side of the definition of stationarity for the input signal $x[k]$ and recalling the linearity of the expectation operator $E\\{\\cdot\\}$ yields\n", "\n", "\\begin{equation}\n", "E\\{ g(y[k_1], y[k_2], \\dots) \\} = E\\{ g(y[k_1 + \\Delta], y[k_2 + \\Delta], \\dots) \\}\n", "\\end{equation}\n", "\n", "where $g(\\cdot)$ denotes an arbitrary mapping function that may differ from $f(\\cdot)$. From the equation above, it can be concluded that the output signal of an LTI system for a stationary input signal is also stationary. The same reasoning can also be applied to an [ergodic](../random_signals/stationary_ergodic.ipynb#Ergodic-Random-Processes) input signal. Since both wide-sense stationarity (WSS) and wide-sense ergodicity are special cases of the general case, the derived results hold also here.\n", "\n", "Summarizing, for an input signal $x[k]$ that is\n", "\n", "* (wide-sense) stationary, the output signal $y[k]$ is (wide-sense) stationary and the in- and output is jointly (wide-sense) stationary\n", "* (wide-sense) ergodic, the output signal $y[k]$ is (wide-sense) ergodic and the in- and output is jointly (wide-sense) ergodic\n", "\n", "This implies for instance, that for a WSS input signal $x[k]$ measures like the auto-correlation function (ACF) can also be applied to the output signal $y[k] = \\mathcal{H} \\{ x[k] \\}$ of an LTI system." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example - Response of an LTI system to a random signal\n", "\n", "The following example computes and plots estimates of the linear mean $\\mu[k]$ and auto-correlation function (ACF) $\\varphi[k_1, k_2]$ for the in- and output of an LTI system. The input $x[k]$ is drawn from a normally distributed white noise process." ] }, { "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", "\n", "L = 64 # number of random samples\n", "N = 1000 # number of sample functions\n", "\n", "# generate input signal (white Gaussian noise)\n", "np.random.seed(1)\n", "x = np.random.normal(size=(N, L))\n", "# generate output signal\n", "h = 2*np.fft.irfft([1,1,1,0,0,0])\n", "y = np.asarray([np.convolve(x[n,:], h, mode='same') for n in range(N)])\n", "\n", "# compute and plot results\n", "def compute_plot_results(x):\n", "\n", " # estimate linear mean by ensemble average\n", " mu = 1/N * np.sum(x, 0)\n", " # estimate the auto-correlation function\n", " acf = np.zeros((L, L))\n", " for n in range(L):\n", " for m in range(L):\n", " acf[n, m] = 1/N * np.sum(x[:, n]*x[:, m], 0)\n", " \n", " plt.subplot(121)\n", " plt.stem(mu)\n", " plt.title(r'Estimate of linear mean $\\hat{\\mu}[k]$')\n", " plt.xlabel(r'$k$')\n", " plt.ylabel(r'$\\hat{\\mu}[k]$')\n", " plt.axis([0, L, -1.5, 1.5])\n", "\n", " plt.subplot(122)\n", " plt.pcolor(np.arange(L), np.arange(L), acf, vmin=-2, vmax=2)\n", " plt.title(r'Estimate of ACF $\\hat{\\varphi}[k_1, k_2]$')\n", " plt.xlabel(r'$k_1$')\n", " plt.ylabel(r'$k_2$')\n", " plt.colorbar()\n", " plt.autoscale(tight=True)\n", "\n", " \n", "plt.figure(figsize = (10, 5))\n", "plt.gcf().suptitle(r'Input signal $x[k]$', fontsize=12)\n", "compute_plot_results(x)\n", "\n", "plt.figure(figsize = (10, 5))\n", "plt.gcf().suptitle(r'Output signal $y[k]$', fontsize=12)\n", "compute_plot_results(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Are the in- and output signals WSS?\n", "* Can the output signal $y[k]$ be assumed to be white noise?\n", "\n", "Solution: From the shown results it can assumed for the input signal $x[k]$ that the linear mean $\\mu_x[k]$ does not depend on the time-index $k$ and that the ACF $\\varphi_{xx}[k_1, k_2]$ does only depend on the difference $\\kappa = k_1 - k_2$ of both time indexes. The same holds also for the output signal $y[k]$. Hence both the in- and output signal are WSS. Although the input signal $x[k]$ can be assumed to be white noise, the output signal $y[k]$ is not white noise due to its ACF $\\varphi_{yy}[k_1, k_2]$." ] }, { "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 }