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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 time-varying 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 5-1 A statistically identical set of binary waveform generators with typical outputs. 3 2 Figure 5-2 Typical sample functions of a random process and illustration of the relative-frequency 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 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) t l t i d t d d 6 autocorrelation does not depend on t 3...
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