{ "cells": [ { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "# Random Signals\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": [ "## Stationary Random Processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Definition\n", "\n", "When the average statistical properties of a random process do not depend on the time index $k$, this process is termed as [*stationary random process*](https://en.wikipedia.org/wiki/Stationary_process). This can be expressed formally as\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 shift of the sample index $k$. Above condition has to hold for all possible mapping functions $f(\\cdot)$. From this definition it becomes clear that\n", "\n", "* random signals of finite length and\n", "* deterministic signals $s[k] \\neq C$ with $C \\in \\mathbb{R}$\n", "\n", "cannot be stationary random processes in a strict sense. However, in practice it is often assumed to be sufficient if above condition holds within a finite interval of sample indexes of a random signal." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cumulative Distribution Functions and Probability Density Functions\n", "\n", "It follows from above definition of a stationary process, that the univariate cumulative distribution function (CDF) of a stationary random process does not depend on the time index $k$\n", "\n", "\\begin{equation}\n", "P_x(\\theta, k) = P_x(\\theta)\n", "\\end{equation}\n", "\n", "the same holds for the univariate probability density function (PDF)\n", "\n", "\\begin{equation}\n", "p_x(\\theta, k) = p_x(\\theta)\n", "\\end{equation}\n", "\n", "The bivariate CDF of two stationary random signals $x[k]$ and $y[k]$ depends only on the difference $\\kappa = k_x - k_y$\n", "\n", "\\begin{equation}\n", "P_{xy}(\\theta_x, \\theta_y, k_x, k_y) = P_{xy}(\\theta_x, \\theta_y, \\kappa)\n", "\\end{equation}\n", "\n", "The same holds for the bivariate PDF\n", "\n", "\\begin{equation}\n", "p_{xy}(\\theta_x, \\theta_y, k_x, k_y) = p_{xy}(\\theta_x, \\theta_y, \\kappa)\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First-Order Ensemble Averages\n", "\n", "According to above definition of stationarity, for the first-order ensemble average of a stationary process the following relation must hold\n", "\n", "\\begin{equation}\n", "E\\{ f(x[k]) \\} = E\\{ f(x[k + \\Delta]) \\}\n", "\\end{equation}\n", "\n", "hence it does not depend on the time index $k$. For the linear mean we consequently yield \n", "\n", "\\begin{equation}\n", "\\mu_x[k] = \\mu_x\n", "\\end{equation}\n", "\n", "and for the variance \n", "\n", "\\begin{equation}\n", "\\sigma_x^2[k] = \\sigma_x^2\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cross- and Auto-Correlation Function\n", "\n", "It follows by introducing the PDF's properties of a stationary process into the definition of the cross-correlation function (CCF) and auto-correlation function (ACF) that\n", "\n", "\\begin{equation}\n", "\\varphi_{xy}[k_x, k_y] = \\varphi_{xy}[\\kappa] = E\\{ x[k] \\cdot y[k-\\kappa]\\} = E\\{ x[k+\\kappa] \\cdot y[k]\\}\n", "\\end{equation}\n", "\n", "and\n", "\n", "\\begin{equation}\n", "\\varphi_{xx}[k_1, k_2] = \\varphi_{xx}[\\kappa] = E\\{ x[k] \\cdot x[k-\\kappa]\\} = E\\{ x[k+\\kappa] \\cdot x[k]\\}\n", "\\end{equation}\n", "\n", "where for the latter $\\kappa = k_1 - k_2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wide-Sense Stationary Random Processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Definition\n", "\n", "The definition of a stationary random process in the previous section must hold for any mapping function $f(\\cdot)$. In practice this cannot be checked in a strict sense. For a wide-sense stationary (WSS) random process the conditions for stationarity must hold only for linear mappings. This leads to the following two conditions a WSS random process has to fulfill\n", "\n", "\\begin{equation}\n", "E\\{ x[k_1] \\cdot x[k_2] \\} = E\\{ x[k_1 + \\Delta] \\cdot x[k_2 + \\Delta] \\}\n", "\\end{equation}\n", "\n", "and\n", "\n", "\\begin{equation}\n", "E\\{ x[k] \\} = E\\{ x[k + \\Delta] \\}\n", "\\end{equation}\n", "\n", "A random signal of finite length cannot be WSS in a strict sense." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example - Evaluation of Wide-Sense Stationarity\n", "\n", "From above definition of a WSS process it is evident that it is sufficient to check the time dependence of the linear mean $x_\\mu[k]$ and the auto-correlation function $\\varphi_{xx}[k_1, k_2]$. Both quantities are estimated and plotted for two different random processes." ] }, { "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 sample functions\n", "np.random.seed(1)\n", "x = np.random.normal(size=(N, L))\n", "x1 = x + np.tile(np.cos(2*np.pi/L*np.arange(L)), [N,1])\n", "h = 2*np.fft.irfft([1,1,1,0,0,0])\n", "x2 = 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 $\\hat{\\mu}_x[k]$')\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 $\\hat{\\varphi}_{xx}[k_1, k_2]$')\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, 4))\n", "plt.gcf().suptitle('Random Process 1', fontsize=12, y=1.05)\n", "compute_plot_results(x1)\n", "\n", "plt.figure(figsize = (10, 4))\n", "plt.gcf().suptitle('Random Process 2', fontsize=12, y=1.05)\n", "compute_plot_results(x2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Which process can be assumed to be WSS? Why?\n", "* Increase the number `N` of sample functions. Do the results support your initial assumption? \n", "\n", "Solution: Inspection of the estimated linear mean $\\hat{\\mu}_x[k]$ for the first random process reveals that it is highly dependent on the sample index $k$. The same holds for the ACF which depends on both sample indexes $k_1$ and $k_2$. For the second random process, the estimated linear mean can be assumed to be approximately zero. Its ACF depends approximately only on the difference $\\kappa = k_1 - k_2$, as can be concluded from the diagonal structures in the plot. Increasing the number of sample functions $N$ increases the certainty of the estimates in the statistical sense." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Higher-Order Temporal Averages\n", "\n", "Ensemble averages are defined as the average across all sample functions $x_n[k]$ for a particular time index $k$. So far, averaging over the sample index $k$ of one sample function was not considered. Such averaging is termed commonly as temporal averaging since the sample index $k$ represents time in many cases. For a stationary process, the higher-order temporal average along the $n$-th sample function is defined as\n", "\n", "\\begin{equation}\n", "\\overline{ f(x_n[k], x_n[k-\\kappa_1], x_n[k-\\kappa_2], \\dots) } = \\lim_{K \\to \\infty} \\frac{1}{2K + 1} \\sum_{k = -K}^{K} f(x_n[k], x_n[k-\\kappa_1], x_n[k-\\kappa_2], \\dots)\n", "\\end{equation}\n", "\n", "where $\\kappa_i \\in \\mathbb{Z} \\; \\forall i$. The introduced statistical measures, like the linear mean, variance and correlation functions, can be computed for each sample function by temporal averaging by using the respective mapping functions $f(\\cdot)$ introduced above. The linear mean as temporal average of the $n$-th sample function $x_n[k]$ is for instance given by\n", "\n", "\\begin{equation}\n", "\\overline{x_n[k]} = \\lim_{K \\to \\infty} \\frac{1}{2K + 1} \\sum_{k = -K}^{K} x_n[k]\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ergodic Random Processes\n", "\n", "An [ergodic process](https://en.wikipedia.org/wiki/Ergodic_process) is a stationary random process whose higher-order temporal averages of all sample functions are equal to the ensemble averages\n", "\n", "\\begin{equation}\n", "\\overline{ f(x_n[k], x_n[k-\\kappa_1], x_n[k-\\kappa_2], \\dots) } = E\\{ f(x[k], x[k-\\kappa_1], x[k-\\kappa_2], \\dots) \\} \\;\\; \\forall n\n", "\\end{equation}\n", "\n", "This implies that all higher-order temporal averages are equal. Any sample function from the process represents the average statistical properties of the entire process. The ensemble averages for a stationary and ergodic random process are given by the temporal averages of one sample function. This result is very important for the practical computation of statistical properties of random signals." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wide-Sense Ergodic Random Processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Definition\n", "\n", "As for a WSS process, the conditions for ergodicity have to hold only for linear mappings $f(\\cdot)$. Under the assumption of a WSS process, the following two conditions have to be met by a wide-sense ergodic random process\n", "\n", "\\begin{equation}\n", "\\overline{ x_n[k] \\cdot x_n[k-\\kappa] } = E\\{ x[k] \\cdot x[k-\\kappa] \\} \\;\\; \\forall n\n", "\\end{equation}\n", "\n", "and\n", "\n", "\\begin{equation}\n", "\\overline{ x_n[k] } = E\\{ x[k] \\} \\;\\; \\forall n\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example - Evaluation of Wide-Sense Ergodicity\n", "\n", "In the following example, the linear mean and autocorrelation function are computed as temporal and ensemble averages for three random processes. The plots show the estimated temporal averages $\\overline{ x_n[k] }$ and $\\overline{ x_n[k] \\cdot x_n[k-\\kappa] }$ on the right-hand side of the sample functions $x_n[k]$. Note, the linear mean as temporal average is a scalar value whose value is illustrated by a bar plot. The estimated ensemble averages $E\\{ x[k] \\}$ and $E\\{ x[k_1] \\cdot x[k_2] \\}$ are shown below the sample functions to indicate the averaging across sample functions." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "L = 64 # number of random samples\n", "N = 10000 # number of sample functions\n", "\n", "# generate sample functions\n", "np.random.seed(11)\n", "x = np.random.normal(size=(N, L))\n", "k = np.arange(L)\n", "x1 = x + np.tile(np.cos(2*np.pi/L*k), [N, 1])\n", "x2 = x + np.tile([np.ones(L), -np.ones(L)], [N//2, 1])\n", "x3 = x + np.ones([N, L])\n", "\n", "# function to 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 by ensemble average\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", " # estimate linear mean as temporal average\n", " mut = 1/L * np.sum(x, 1)\n", " # estimate the auto-correlation function as temporal average\n", " acft = np.zeros((N, L))\n", " for n in range(N):\n", " acft[n, :] = np.correlate(x[n, :], x[n, :], mode='same')\n", " kappa = np.arange(L) - L//2\n", " \n", " for n in range(2):\n", " plt.figure(figsize = (10, 5))\n", " plt.subplot(131)\n", " plt.stem(x[n, :])\n", " plt.title(r'Sample function $x_%d[k]$'%n)\n", " plt.xlabel(r'$k$')\n", " plt.ylabel(r'$x_%d[k]$'%n)\n", " plt.axis([0, L, -4, 4])\n", "\n", " plt.subplot(132)\n", " plt.bar(-0.4, mut[n])\n", " plt.title(r'Linear mean $\\overline{ x_%d[k] }$'%n)\n", " plt.ylabel(r'$\\hat{\\mu}_{x,%d}$'%n)\n", " plt.axis([-.5, .5, -1.5, 1.5])\n", " \n", " plt.subplot(133)\n", " plt.stem(kappa, acft[n, :])\n", " plt.title(r'Autocorrelation $\\overline{ x_%d[k] \\cdot x_%d[k-\\kappa] }$'%(n,n))\n", " plt.xlabel(r'$\\kappa$')\n", " plt.ylabel(r'$\\hat{\\varphi}_{xx,%d}[\\kappa]$'%n)\n", " plt.axis([-L//2, L//2, -30, 150])\n", " plt.tight_layout()\n", " \n", " plt.figure(figsize = (10, 5))\n", " plt.subplot(131)\n", " plt.stem(mu)\n", " plt.title(r'Linear mean $E\\{ x[k] \\}$')\n", " plt.xlabel(r'$k$')\n", " plt.ylabel(r'$\\hat{\\mu}[k]$')\n", " plt.axis([0, L, -1.5, 1.5])\n", " \n", " plt.figure(figsize = (4, 4))\n", " plt.pcolor(k, k, acf, vmin=-2, vmax=2)\n", " plt.title(r'ACF $E\\{ x[k_1] \\cdot x[k_2] \\}$')\n", " plt.xlabel(r'$k_1$')\n", " plt.ylabel(r'$k_2$')\n", " plt.colorbar()\n", " plt.autoscale(tight=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Random Process 1**" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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C8by8fonE9srCLAxpPKQt4PPyhiELszCk8ZC2gPc8CkMWZmFI4yFtAe95FIYszMKQxkPaAj4vbxhCu+5ovbx2twXihvItO4ZGZkf32t32CGlalHp5SFukd8qkkbBec94sFi/fyMeXrPHmmBbI0gDvNB7SFvOB4K2VtQHeafyctMV8IHhrZW2AdxoPaYt5c0xrZW2AdxoPaYt5c0xrZW2Ad5rslDQnfCB4a2VtgHcaD2mL+UDw1sraAO80HtI28IHgrZWlAd5pvAnG5VLW20aTPKQud6q1jWaRh7SNfCB4c+ShbTTJQ9om8UDweJyp9zxqnDy0jSbVVXEkaWodt55mFzZPfCB48+ShbTSp3j3pS9Gt2pF9JzBr3CUqCO951Dy3XHrqIeekkL220aR6Q7rBzPqrbSBpdQPKUxgTOztSg+o9j8av/OrdfRmv3a13/1/PlXD9arlj4APBmyvrbaNJdYXUzN4EkPS/yh+T1JncxtWnd8okZvdO9p5Hrqaxnkn3SbomXpD0G8AjjS3SyHNfJmmjpE2SFqY8PknSkujxxyWd2IxyNFPvlEkjv/a3XHoqi5dvZPbCB7ng1hU+3acbMdYmmOuB5ZKeAwz4OvCpRhcq2jt/BbgE2Ao8KWmZmT2b2OxDwOtmdoqkq4EvAO9vdFlawQeCN04WZ6ivpd4mmG9KuonSeedHgDuA24D5ZvZgE8p1HrDJzJ43s33At4Aryra5Arg7un8fcJGkTPYr8YHgjRH3NIonIc/KDPW1yMxqbyTNA86JbmcDJwFPAiuB9WZ2X0MLJb0XuMzMPhwt/2fgfDO7MbHN+mibrdHyc9E22ys975yjeuzL510IwBnTj+LZl98YdT/WqHX1/M0bQ/srFZnjjj4CgBPfMpkXXtt9yGONWpeX59n2q70Mlzc+A5MmdDKpq7Q/auXnmrbulWkz+eA9fw2ApKfMbGBUgcvUdbhrZiuAFfGypAnA6ZRCez6lPVmQJC0AFgCcMuUojpz467GFle43el2tx3fvPVDxy7Vn36/3sMn7jV6Xh+dJ+z8E2HtgmGMmd40st+pzTVs3dfLYa5nr2pO2mqS5wGfM7NJoeRGAmX0+sc3yaJvHoh+NV4BpVuUNDQwM2KpVq5pb+MNQ3iEcSo3vX7rq3JHpJ5dcP5f33/7YIX/XqHV5eZ7VL+5MbXvu6+lm5cJ5o9a3W7170nrPSf+tEduMwZPAHEmzJU0ErgaWlW2zDLg2uv9eYEW1gIYsHpjc19ONyM6kzaHJ66wX9dbuni5pLaVugWlBEHB0owplZgck3Qgsp9Td8C4ze0bSZ4FVZrYM+Brwd5I2ATsoBTmz5vf3jYSyfI/h6tM7ZRJ/Mm/OIeNI8zCyqN6QnlbHNqNPGMbBzB4CHipb92eJ+28C72vka7rsS/7Y5UW9FUc/B5C0DlibuK0DrjWzzzWthAWzdPXgyLnVBbeuyHSfU9cYVc9JJZ0p6R8Sq/4j8FVgiNLh5Xrgnc0rXrHEFUhx5cfgziE2b9/N9l1721yysG3ftZfVL+7k8c07ctlbq9ae9BESHefNbAfwg+iGpDnAf2tS2QonbzMKtEIRBs/Xqt19BzByKCvpN5MPmtnPKHVucA2QtxkFWqEIg+er7knNbB3wgcSq2yWdDAxSOic9Algv6Ugz29O8YhbDjJ5uBlOCmtUZBVqhCIPnx/Tpm9nbzWwWpY7s3wM2Ad3AGkk/bUL5CiUPs623WhEu23FYE5GZ2YvAi8B343WSpjSqUEUVn0PlZb7YVpg5tfuQc1LIRweGpIbNFmhmuxr1XEVW3s7nHRsqW7p6cOSctFNi2CyXV1H3KT0D5m2mlcVjcONz0mGzkT1ongIKfi2YYHmbaXVFGoPrIQ2Ut5lWV4Ra3ZiHNFDeZlpdEWp1Yx7SQOVtFvZGy+uwtDT+iQfK20yriy/GHI/BzfOUqF67GyhvM60tj8PS0nhIA+Ztpg78cNe54PmeNCOSHRsm5mTS58OxfddetuwYGungkcfOC+U8pBlQ3rEhL5M+j1URxo6m8cPdDKjUsSGPvWuqKcLY0TQe0gyo1LEhj71rqilSL6MkD2kGVOrYkMfeNdUUqZdRkoc0Ayp1bMhj75pqinrhZQ9pBvgM9yXxhZeL0MsoyWt3M8JnuC/pnTKJJdfPrb1hjvie1LnAeUhdJsSdOfI6AXY1fribMUWcUqV8qpSidGKI+Z40Q4o6pUqRpkpJ4yHNkKJOqVLUTgwxD2mGFHVKlaJ2Yoh5SDOkqFOqFGmqlDT5/nRzpqhTqhRpqpQ0XrubIUWeUqUoU6Wk8ZBmTPLLunT1IJ+8by3Pbdudy4HgRRzgncZDmlF5Hwhe1AHeaYI7J5U0VdLDkn4W/XtMhe2GJa2JbstaXc52y/tA8KIO8E4TXEiBhcCjZjYHeDRaTjNkZudGt8tbV7ww5H0geNHbRpNCDOkVwN3R/buB+W0sS7DyPhC86G2jSSGG9Fgzezm6/wpwbIXtjpC0StJPJBUuyHkfCF7UAd5p2lJxJOkR4LiUhz6dXDAzk2Qp2wGcYGaDkk4CVkhaZ2bPpbzWAmABwKxZs8ZZ8nCUN8d0RbW78/v7uOeJF9tcuvGLm5Xe3H9wpLnJa3dbyMwurvSYpF9Imm5mL0uaDrxa4TkGo3+fl/QDoB8YFVIzuwO4A2BgYKBS4DMp7wPBizjAO02Ih7vLgGuj+9cCD5RvIOkYSZOi+73ABcCzLSuhcy0UYkhvBS6R9DPg4mgZSQOS7oy2OR1YJelp4PvArWZW2JCWD4jO+tC1Ig/wThNcZwYzew24KGX9KuDD0f1/Bc5qcdGClDbGNK5wyWJ3waIP8E4T4p7UjUHexpgWfYB3Gg9pxuVtjKl3YhjNQ5pxeRtj6p0YRsvmJ+lG5G2MadEHeKfxkGZc+ez2fT3dzO6dnMlKI/AB3mmCq911Y5eHMabJqUq3vj5U2N5FaXxPmiNZHWNaqdkl9HK3ioc0R7I6xtSbXarzkOZIVseYerNLdR7SHMnqGFNvdqnOQ5ojac0xAHv2HQi6P683u1TnIc2RuDmmp7vrkPWv79kf9DVjvNmlOm+CyZn5/X0sXr6RnUP7D1kf9+cNtf20yPPq1uJ70hzKSn/e7bv2+pC0OnhIcygL/XnjeXW9bbS2cD411zBZ6M/r8+rWz89JcygL14zxttH6eUhzqrwiJqSJyqod0nrb6Gge0gJIdl5vd6f7uJ9uGm8bTechzbnQOt3HV0kr1yl522gFXnGUc6F1uq90LnrQzANagYc05ypVxAzuHGpLDyTvpzt2fribczN6uhmsENTN23e3rBzJCwILSLa++Llodb4nzblKne6hdVN/lndcMCC+FpP3063N96Q5F3/5b1qyJvXxVnQVTOu4YJQCunLhvKa/ftb5nrQA5vf30dfGroLecWF8PKQF0a6ugt5xYfw8pAVRPvVnT3cXHRLPbdvdtIs8eceFxvBz0gKJuwrGHRwORCeKzbrIk3dcaAzfkxZQqy7y5B0XGsNDWkCtGhTuHRcaw0NaQNVCsvrFneM+P41nXIg7LiT5uejYeUgLqFoHh/F2wPeOC43nFUcFlBwUntZl8KDBzfc+zYm9R465Isk7LjSe70kLan5/HysXzht1OBobNhvzNKBLVw96x4Um8D1pwVXrgH/Q4IXX9ow0pVxw64qK07BUaxONX8cdHt+TFly181OA4YN2yIx+5XvXeNaH57btHtWsE/PKovEJLqSS3ifpGUkHJQ1U2e4ySRslbZK0sJVlzJO4J1KnKh34HirZnlp+ycJKvLJofEI83F0PXAncXmkDSZ3AV4BLgK3Ak5KWmdmzrSlivsQBWnT/uop7w6R9wwd5fPOOup67r6fbAzpOwYXUzDYAqPov+3nAJjN7Ptr2W8AVgIf0MNWq8T0cfpjbGMEd7tapD9iSWN4arRtF0gJJqySt2rZtW0sKl1VxjW+lYW1j4W2ijdOWkEp6RNL6lNsVjX4tM7vDzAbMbGDatGmNfvpcqlWZVE13Vyd/+f5zWblwnge0QdpyuGtmF4/zKQaBmYnl46N1rgHSZsDfs+8Ar+/ZX/Xv+nq6ueXSUz2cDRbcOWmdngTmSJpNKZxXA7/f3iLlS/kM+PHwtrSKpe6uTj+0baLgzkklvVvSVmAu8KCk5dH6GZIeAjCzA8CNwHJgA3CvmT3TrjIXQXLQODDSZOPnns0nM6u9VU4MDAzYqlWr2l0M5wCQ9JSZVewLEAtuT+qcO5SH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnAeUidC5yH1LnABRdSSe+T9Iykg5IGqmz3gqR1ktZIWtXKMjrXShPaXYAU64Ergdvr2PbtZra9yeVxrq2CC6mZbQCQ1O6iOBeE4A53x8CA/yvpKUkL2l0Y55qlLXtSSY8Ax6U89Gkze6DOp/kdMxuU9BvAw5J+amY/THmtBUAc4r2S1h9eqYPTC+TlUD9P7wXqfz8n1PNkMrPxFadJJP0A+ISZ1awUkvQZYJeZ/e8a260ys4qVUVni7yVcjX4/mTzclTRZ0r+L7wPvoFTh5FzuBBdSSe+WtBWYCzwoaXm0foakh6LNjgV+LOlp4AngQTP7l/aU2LnmCrF29zvAd1LWvwS8M7r/PHDOYTz9HeMrXVD8vYSroe8n2HNS51xJcIe7zrlDFSKkki6TtFHSJkkL212esZI0U9L3JT0bdZn8WLR+qqSHJf0s+veYdpe1XpI6Ja2W9L1oebakx6PPaImkie0uYz0k9Ui6T9JPJW2QNLfRn0vuQyqpE/gK8LvAGcA1ks5ob6nG7ABws5mdAbwN+Ej0HhYCj5rZHODRaDkrPgZsSCx/Afg/ZnYK8DrwobaUauz+CvgXMzuNUj3JBhr9uZhZrm+UaomXJ5YXAYvaXa5xvqcHgEuAjcD0aN10YGO7y1Zn+Y+PvrzzgO8BotT4PyHtMwv1BhwNbCaq20msb+jnkvs9KdAHbEksb43WZZKkE4F+4HHgWDN7OXroFUpNU1nwl8AngYPR8luAnWZ2IFrOymc0G9gGfD06dL8zardv6OdShJDmhqQpwLeBm8zsjeRjVvrZDr6qXtK7gFfN7Kl2l6UBJgC/BdxmZv3AbsoObRvxuRQhpIPAzMTy8dG6TJHURSmg/2Bm90erfyFpevT4dODVdpVvDC4ALpf0AvAtSoe8fwX0SIrb7bPyGW0FtprZ49HyfZRC29DPpQghfRKYE9UeTgSuBpa1uUxjotK4va8BG8zsS4mHlgHXRvevpXSuGjQzW2Rmx5vZiZQ+ixVm9gHg+8B7o82y8l5eAbZIOjVadRHwLA3+XArRmUHSOymdB3UCd5nZ59pcpDGR9DvAj4B1/Po87k8pnZfeC8wCfg5cZWY72lLIwyDpQkqDKN4l6SRKe9apwGrgD8xsbzvLVw9J5wJ3AhOB54EPUtr5NexzKURIncuyIhzuOpdpHlLnAuchdS5wHlLnAuchdS5wHlLnAuchdS5wHlJXN0kXSfq7dpejaDykbizOodQbyLWQh9SNxTnAakmTJH1D0p/LrwfSdMHNFuiCdjalER3LgTvN7O/bXJ5C8L67ri7RULntlDqMX29mj7W5SIXhh7uuXqdTGvZ3ABhuc1kKxUPq6nUO8K+UxoB+XVJWpmrJPA+pq9c5wHoz+3/Ap4B7o0Ng12R+Tupc4HxP6lzgPKTOBc5D6lzgPKTOBc5D6lzgPKTOBc5D6lzgPKTOBe7/A6VDeho0NGwqAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "compute_plot_results(x1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Random Process 2**" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "compute_plot_results(x2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Random Process 3**" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "compute_plot_results(x3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Which process can be assumed to be stationary and/or ergodic? Why?\n", "\n", "Solution: The linear mean $\\mu_x[k]$ estimated by the ensemble average of the first process depends on the sample index $k$. Consequently, this process is not stationary and also not ergodic. Inspection of the linear mean and auto-correlation function estimated by the ensemble averages of the second random process reveals that this processed can be assumed to be WSS. The linear mean as temporal average of the sample functions is not constant with respect to the sample functions. Consequently, this process can be assumed to be WSS but not ergodic. The third process can be assumed to be wide-sense stationary and ergodic." ] }, { "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 }