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