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STOCHASTIC PROCESSES
Lecturer Prof. Jovan Elazar
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Introduction
Probability
Random variables
Multiple random variables
Function of random variables
Random processes
Analysis and processing of random processes
Recommended textbook: Hwei P. Hsu, Probability, Random
Variables, and Random Processes, Schaum’s Outline Series,
McGraw Hill
Stochastic Processes - Introduction
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SIGNALS: DETERMINISTIC VS. STOCHASTIC
Deterministic Signals
Deterministic Signal
So far we have encountered only deterministic signals.
They can be determined by a
 mathematical expression
 rule,
 table
Future values can be calculated from past values.
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Stochastic Signals
Random Signal
Stochastic signals, or random signals, cannot be characterized
by a simple, well-defined mathematical expression.
We must use probability and statistics to analyze their behavior.
Average value, from a collection of signals, is usually studied
(rather than one individual signal).
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Random Process
In order to study random signals we have to look at a collection
of these signals. This collection of signals is called a random
process.
RANDOM PROCESS:
A family or ensemble of signals that
correspond to every possible outcome of a certain signal
measurement.
Each signal in this collection is referred to as a realization or
sample function of the process.
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Random Sinusoidal Process
f [n]  A sin( n   )
Amplitude and phase are random
Stochastic Processes - Introduction
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