{
"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": [
"## White Noise"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Definition\n",
"\n",
"[White noise](https://en.wikipedia.org/wiki/White_noise) is a wide-sense stationary (WSS) random signal with constant power spectral density (PSD)\n",
"\n",
"\\begin{equation}\n",
"\\Phi_{xx}(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega}) = N_0\n",
"\\end{equation}\n",
"\n",
"where $N_0$ denotes the power per frequency. White noise draws its name from the analogy to white light. It refers typically to an idealized model of a random signal, e.g. emerging from measurement noise. The auto-correlation function (ACF) of white noise can be derived by inverse discrete-time Fourier transformation (DTFT) of the PSD\n",
"\n",
"\\begin{equation}\n",
"\\varphi_{xx}[\\kappa] = \\mathcal{F}_*^{-1} \\{ N_0 \\} = N_0 \\cdot \\delta[\\kappa]\n",
"\\end{equation}\n",
"\n",
"This result implies that white noise has to be a zero-mean random process. It can be concluded from the ACF that two neighboring samples $k$ and $k+1$ are uncorrelated. Hence they show no dependencies in the statistical sense. Although this is often assumed, the probability density function (PDF) of white noise is not necessarily given by the normal distribution. In general, it is required to additionally state the amplitude distribution when denoting a signal as white noise."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example - Amplifier Noise\n",
"\n",
"Additive white Gaussian noise (AWGN) is often used as a model for amplifier noise. In order to evaluate if this holds for a typical audio amplifier, the noise $n[k]$ captured from a microphone preamplifier at full amplification with open connectors is analyzed statistically. For the remainder, a function is defined to estimate and plot the PDF and ACF of a given random signal."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats as stats\n",
"\n",
"\n",
"def estimate_plot_pdf_acf(x, nbins=50, acf_range=30):\n",
" \"\"\"Estimate and plot PDF/CDF of a given sample function.\"\"\"\n",
"\n",
" # compute and truncate ACF\n",
" acf = 1 / len(x) * np.correlate(x, x, mode=\"full\")\n",
" acf = acf[len(x) - acf_range - 1 : len(x) + acf_range - 1]\n",
" kappa = np.arange(-acf_range, acf_range)\n",
"\n",
" # plot PDF\n",
" plt.figure(figsize=(10, 6))\n",
" plt.subplot(121)\n",
" plt.hist(x, nbins, density=True)\n",
" plt.title(\"Estimated PDF\")\n",
" plt.xlabel(r\"$\\theta$\")\n",
" plt.ylabel(r\"$\\hat{p}_n(\\theta)$\")\n",
" plt.grid()\n",
"\n",
" # plot ACF\n",
" plt.subplot(122)\n",
" plt.stem(kappa, acf)\n",
" plt.title(\"Estimated ACF\")\n",
" plt.ylabel(r\"$\\hat{\\varphi}_{nn}[\\kappa]$\")\n",
" plt.xlabel(r\"$\\kappa$\")\n",
" plt.axis([-acf_range, acf_range, 1.1 * min(acf), 1.1 * max(acf)])\n",
" plt.grid()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now the pre-captured noise is loaded and analyzed"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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"