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DSP_ch8 - DSP EEE 407/591 by Andreas Spanias Ph.D Chapter 8...

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1 Copyright (c) Andreas Spanias Ch 8 - 1 DSP EEE 407/591 by Andreas Spanias, Ph.D. Chapter 8 [email protected] http://www.eas.asu.edu/~spanias Copyright (c) Andreas Spanias Ch 8 - 2 Introduction to Random Signal Processing Deterministic Signals: are characterized explicitly by a mathematical equation and their value at any time can be predicted exactly. Random Signals: are not modeled explicitly by a mathematical equation, however, they are usually characterized by their statistics. Most “real-life” signals, such as those encountered in speech, communications,, and radar are random Our discussion concentrates on signals whose D.C. content and power spectra do not change with time are constant. Also we will be concerned with signals. whose statistics can be measured by time averaging. We call such signals wide-sense stationary and ergodic .
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2 Copyright (c) Andreas Spanias Ch 8 - 3 Random Signal Processing - Some Definitions µ x N n N N E x n N x n = = + → ∞ = − [ ( )] ( ) lim 1 2 1 The mean is defined as: Statistical expectation; for ergodic signals it is computed as a time average The variance σ µ µ µ x x x x E x n x n E x n 2 2 2 = = [( ( ) )( ( ) )] [ ( )] The variance is a measure of dispersion from the mean Copyright (c) Andreas Spanias Ch 8 - 4 The mean, , is the DC component. The mean squared is the DC power. The mean square is the total average power. The variance is the AC power. The standard deviation is the rms value. µ x µ x 2 E x n [ ( )] 2 σ x 2 σ x Examples, Interpretations, and Analogies to electrical signals 0 10 20 30 40 50 60 70 80 90 100 -4 -3 -2 -1 0 1 2 3 σ 2 1 > σ 2 2 σ 2 1 σ 2 2 µ 1 = µ 2 =0
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