1 11 Lecture 14 Random Signals and Noise (I) Fall 2008 NCTU EE Tzu-Hsien Sang

2 Outline Terminology of Random Processes Correlation and Power Spectral Density Linear Systems and Random Processes Narrowband Noise

3 Random Processes Informal Definition: The outcomes ( events ) of a chance experiment are mapped into functions of time ( waveforms ). Cf.: Random variables: outcomes are mapped into numbers. Note: Each waveform is called a sample function, or a realization. The totality of all sample functions is called an ensemble. Q: Let’s try to build an axiomatic theory. What will you do?

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12 Wide-sense stationary (WSS): It is extremely difficult to verify whether a random process is stationary or not. For practical purposes, often WSS is good enough. A random process X(t) is wide-sense stationary if E[X(t)] = constant, and E[X(t)X*(t+  )] = R X (  ) function of  only. Remarks: (i) strict-sense stationary  wide-sense stationary (ii) For Gaussian random processes, WSS = strict- sense stationary ( A Gaussian process has only two parameters: mean and covariance )

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