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Unformatted text preview: 1 EEN 404 EEN 404 Communication Systems Communication Systems 1 Ch6 Random Signals and Noise Ch6 Random Signals and Noise Random Processes (r.p.) 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 timevarying r.p.: an outcome of a chance experiment, i , is mapped to function of time 2 X(t, i ) called sample function The totality of all sample functions is called an ensemble The underlying chance experiment is called a random process, or we use X(t, ) to denote an r. p. For specific time t j , X(t j , ) is a random variable For fixed t= t j and fixed = j , X(t j , i ) is a number r.v.: an outcome is mapped to a number X( i ) , we use X( ) to denote an r.v. We often suppress in X(t, ) and X( ) => X(t) or X Figure 51 A statistically identical set of binary waveform generators with typical outputs. 3 2 Figure 52 Typical sample functions of a random process and illustration of the relativefrequency interpretation of its joint pdf. 4 (a) Ensemble of sample function. (b) Superposition of the sample functions shown in (a). Ensemble average mean function: variance function: autocorrelation function: 5 Strictsense stationary process: the pdf is time shiftinvariant any order of statistics of X(t) is timeinvariant Widesense stationary (WSS) processes: the mean of X(t) is constant (does not depend on t) t l t i d t d d 6 autocorrelation does not depend on t 3...
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 Spring '10
 X.CAI

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