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Random Processes and PSD

Random Processes and PSD. Analog and Digital Communications Autumn 2005-2006. Random Processes. Cross-correlation (Processes are orthogonal if ) Cross-covariance. Example. Example. Mean is constant and autocorrelation is dependent on. Example. Stationary and WSS RP.

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Random Processes and PSD

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  1. Random Processes and PSD Analog and Digital Communications Autumn 2005-2006 CS477: Analog and Digital Communications

  2. Random Processes • Cross-correlation (Processes are orthogonal if ) • Cross-covariance CS477: Analog and Digital Communications

  3. Example CS477: Analog and Digital Communications

  4. Example Mean is constant and autocorrelation is dependent on CS477: Analog and Digital Communications

  5. Example CS477: Analog and Digital Communications

  6. Stationary and WSS RP • Stationary Random Process (RP) • Wide sense stationary (WSS) RP • Mean constant in time • Autocorrelation depends only on • Stationary  WSS (Converse not true!) CS477: Analog and Digital Communications

  7. Power Spectral Density (PSD) • Defined for WSS processes • Provides power distribution as a function of frequency • Wiener-Khinchine theorem • PSD is Fourier transform of ACF CS477: Analog and Digital Communications

  8. PSD: Example CS477: Analog and Digital Communications

  9. Deterministic Signals and PSD For energy signals, multiply above expression with time ACF is a more generic function than average power CS477: Analog and Digital Communications

  10. Deterministic Signals Cross-correlation function Cross power spectral density (Also applicable to jointly stationary random signals) CS477: Analog and Digital Communications

  11. LTI Systems Revisited For random and deterministic signals: (Prove it at home!) (For real channels!) CS477: Analog and Digital Communications

  12. LTI Example: Random Signal Consider White Noise input to an LTI filter CS477: Analog and Digital Communications

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