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copyright Robert J. Marks II ECE 5345 Analysis & Processing of Random Signals copyright Robert J. Marks II

Analysis & Processing of Random Signals Power Spectral Density of a WSS process is the Fourier transform of its autocorrelation “Spectral” a function of frequency “Power Density” Integration gives power copyright Robert J. Marks II

Power Spectral Density Inverse Transform: “Spectral” a function of frequency “Power Density” Integration gives power copyright Robert J. Marks II

Power Spectral Density Properties follows from even autocorrelation follows from even autocorrelation proof to follow copyright Robert J. Marks II

Power Spectral Density Properties thus copyright Robert J. Marks II

Power Spectral Density The power in a specified frequency band is obtained by integrating the PSD copyright Robert J. Marks II

Power Spectral Density Example: Random telegraph signal copyright Robert J. Marks II

Power Spectral Density Example: Random telegraph signal copyright Robert J. Marks II

Power Spectral Density of Discrete RP’s Let X[n] be WSS. The PSD is the DTFT of the autocorrelation. SX(f) has the PSD properties except integration is from (-1/2, 1/2). Like all DTFT’s, SX(f) is periodic with period one. copyright Robert J. Marks II

Power Spectral Density Types of Noise Continuous White Noise Discrete White Noise Laplace Noise copyright Robert J. Marks II

copyright Robert J. Marks II Types of Noise Continuous White Noise copyright Robert J. Marks II

copyright Robert J. Marks II Types of Noise Continuous White Noise Thermal Noise. Infinite Power! White Gaussian Noise copyright Robert J. Marks II

copyright Robert J. Marks II Types of Noise Discrete White Noise Notes: Finite Power. Not samples from CWN. copyright Robert J. Marks II

copyright Robert J. Marks II Types of Noise Discrete White Noise Source: iid sequence. Finite Power. Not samples from CWN. copyright Robert J. Marks II

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