wide_sense_stationary_processes

# wide_sense_stationary_processes - 2.2. Wide-Sense...

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2.2. Wide-Sense Stationary (WSS) Processes Mean of the random process X ( t ) is the mean of random variable X ( t ) at time instant t . + = dx x xf t X E t X ) ( )] ( [ ) ( ) ( )] ( [ t t X E X μ = Let f X(t ) ( x ) be the pdf of X ( t ) at time instant t . Autocorrelation function of X ( t ) is a function of two variables t 1 = t and t 2 t + τ , )] ( ) ( [ ) , ( τ τ + = + t X t X E t t R X This is a measure of the degree to which two time samples of the same random process are related

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Autocorrelation function of X ( t ) is a function of two variables t 1 = t and t 2 = t + τ , )] ( ) ( [ ) , ( τ τ + = + t X t X E t t R X This is a measure of the degree to which two time samples of the same random process are related
A random process X ( t ) is WSS if ) ( )] ( ) ( [ ) , ( ) ( constant )] ( [ ) ( ) ( τ τ τ μ X X X R t X t X E t t R ii t X E t i = = = = What is a WSS Process? In other words, a random process X ( t ) is WSS if its two statistics, its mean and autocorrelation, do not vary with a shift in the time origin.

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Solution.
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## This note was uploaded on 10/28/2009 for the course MATH ma024 taught by Professor Thu during the Spring '09 term at Vienna EBA.

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wide_sense_stationary_processes - 2.2. Wide-Sense...

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