Chapter 15: Linear Systems with Random Inputs

Learning Objectives

• Prove that a WSS process through a BIBO-stable LTI system produces a WSS output, and derive the output mean, autocorrelation, and PSD
• State and prove the matched filter theorem: the filter maximizing output SNR for a known signal in AWGN
• Derive the non-causal Wiener filter as the LMMSE estimator in the frequency domain via the Wiener-Hopf equation
• Define noise equivalent bandwidth and compute it for standard filter shapes
• Apply these results to receiver design, channel estimation, and noise analysis in communication systems