ch6_rsn - EEN EEN 404 Communication Systems Ch6 Random...

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EEN 404 Communication Systems h6 Random Signals and Noise Ch6 Random Signals and Noise 1

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Random Processes (r.p.) h l i i ti t d t d l ith ti when analyzing communication systems, one needs to deal with time- varying signals (processes) thermal noise in electronic circuit reflection of radio waves from different layers => the received signal is random and time-varying r.p.: an outcome of a chance experiment, ζ i , is mapped to function of time X(t, ζ i ) called sample function he totality of all sample functions is called an semble The totality of all sample functions is called an ensemble The underlying chance experiment is called a random process, or we use X(t, ζ ) to denote an r. p. i f i t i t X(t i d ib l For specific time t j , X(t j , ζ ) is a random variable For fixed t= t j and fixed ζ = ζ j , X(t j , ζ i ) is a number r.v.: an outcome is mapped to a number X( ζ ) , we use X( ζ ) to denote an r.v. 2 i We often suppress ζ in X(t, ζ ) and X( ζ ) => X(t) or X
Figure 5-1 A statistically identical set of binary waveform generators ith t i l t t with typical outputs. 3

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Figure 5-2 Typical sample functions of a random process and illustration fth l ti of the relative-frequency interpretation of its joint pdf. (a) Ensemble of sample function. ) Superposition of the sample (b) Superposition of the sample functions shown in (a). 4
Ensemble average • mean function: • variance function: • autocorrelation function: 5

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Strict-sense stationary process: the pdf is time shift-invariant any order of statistics of X(t) is time-invariant Wide-sense stationary (WSS) processes: the mean of X(t) is constant (does not depend on t) autocorrelation does not depend on t 6
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ch6_rsn - EEN EEN 404 Communication Systems Ch6 Random...

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