{
"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": [
"## Introduction\n",
"\n",
"Random signals are signals whose values are not (or only to a limited extend) predictable. Frequently used alternative terms are\n",
"\n",
"* stochastic signals\n",
"* non-deterministic signals\n",
"\n",
"Random signals play an important role in various fields of signal processing and communications. This is due to the fact that only random signals carry information. A signal which is observed by a receiver has to be unknown to some degree in order to represent novel [information](https://en.wikipedia.org/wiki/Information).\n",
"\n",
"Random signals are often classified as useful/desired and disturbing/interfering signals. For instance\n",
"\n",
"* useful signals: data, speech, music, images, ...\n",
"* disturbing signals: thermal noise at a resistor, amplifier noise, quantization noise, ...\n",
"\n",
"Practical signals are frequently modeled as a combination of useful signals and additive noise.\n",
"\n",
"As the values of a random signal cannot be foreseen, the properties of random signals are described by the their statistical characteristics. One measure is for instance the average value of a random signal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Example - Random Signals**\n",
"\n",
"The following audio examples illustrate the characteristics of some deterministic and random signals. Lower the volume of your headphones or loudspeakers before playing back the examples.\n",
"\n",
"1. Cosine signal\n",
"\n",
" [./cosine.wav](./cosine.wav)\n",
"2. Noise\n",
"\n",
" [./noise.wav](./noise.wav)\n",
"3. Cosine signal superpositioned by noise\n",
"\n",
" [./cosine_noise.wav](./cosine_noise.wav)\n",
"4. Speech signal\n",
"\n",
" [../data/speech.wav](../data/speech.wav)\n",
"5. Speech signal superpositioned by noise\n",
"\n",
" [./speech_noise.wav](./speech_noise.wav)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Excercise**\n",
"\n",
"* Which example can be considered as deterministic, random signal or combination of both?\n",
"\n",
"Solution: The cosine signal is the only deterministic signal. Noise and speech are random signals, as their samples can not (or only to a limited extend) be predicted from previous samples. The superposition of the cosine and noise signals is a combination of a deterministic and a random signal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Processing of Random Signals\n",
"\n",
"In contrary to the assumption of deterministic signals in traditional signal processing, [statistical signal processing](https://en.wikipedia.org/wiki/Statistical_signal_processing) treats signals explicitly as random signals. Two prominent application examples involving random signals are"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Measurement of physical quantities\n",
"\n",
"The measurement of physical quantities is often subject to additive noise and distortions. The additive noise models e.g. the sensor noise. The distortions, by e.g. the transmission properties of an amplifier, may be modeled by a system.\n",
"\n",
"![Model for the measurement of physical quantities](measurement_channel.png)\n",
"\n",
"$\\mathcal{H}$ denotes an arbitrary (not necessarily LTI) system. The aim of statistical signal processing is to estimate the physical quantity from the observed sensor data, given some knowledge on the disturbing system and the statistical properties of the noise."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Communication channel\n",
"\n",
"In communications engineering a message is sent over a channel distorting the signal by e.g. multipath propagation. Additive noise is present at the receiver due to background and amplifier noise.\n",
"\n",
"![Model for the transmission of a message over a communication channel](communication_channel.png)\n",
"\n",
"The aim of statistical signal processing is to estimate the send message from the received message, given some knowledge on the disturbing system and the statistical properties of the noise."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Random Processes\n",
"\n",
"A random process is a [stochastic process](https://en.wikipedia.org/wiki/Stochastic_process) which generates an ensemble of random signals. A random process\n",
"\n",
"* provides a mathematical model for an ensemble of random signals and\n",
"* generates different sample functions with specific common properties.\n",
"\n",
"It is important to differentiate between an\n",
"\n",
"* *ensemble*: collection of all possible signals of a random process and an\n",
"* *sample function*: one specific random signal.\n",
"\n",
"An example for a random process is speech produced by humans. Here the ensemble is composed from the speech signals produced by all humans on earth, one particular speech signal produced by one person at a specific time is a sample function."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Example - Sample functions of a random process**\n",
"\n",
"The following example shows sample functions of a continuous amplitude real-valued random process. All sample functions have the same properties with respect to certain statistical measures."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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