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Analysis and Processing of Random Signals
Part 2
Contents
• Sampling of Bandlimited Random Processes
• Estimating the PSD
• Optimum Linear Systems
Sampling of Bandlimited RP
• Sampling theorem for deterministic signals: Review
Sampling of Bandlimited RP
Sampling of Bandlimited RP
Sampling of Bandlimited RP
Sampling of Bandlimited RP
Sampling a WSS RP
Digital Filtering of a Sampled WSS RP
Amplitude Modulation by Random Signals
X(t): Bandpass Signal
Amplitude Modulation by Random Signals
Estimating the PSD
Estimating the PSD
• Variance of Periodogram Estimate
• Smoothing of Periodogram Estimate
Estimating the PSD
Optimum Linear Systems
Xalpha : Discrete-time zero-mean process
Optimum Linear Systems
• Orthogonality Condition
Optimum Linear Systems
Optimum Linear Systems
• Prediction
Optimum Linear Systems
• Wiener-Hopf equations
Zt is to be estimated using only the past and present of Xalpha
• The optimum linear systems considered have two limitations:
1) Assumption of WSS Signals
2) The number of equations grows with the size of the observation set
Solution Kalman Filter