Chapter 16: Mean-Square Calculus and Bandlimited Processes

Learning Objectives

• Define mean-square continuity, differentiation, and integration, and relate them to autocorrelation smoothness
• Prove that the PSD of the mean-square derivative is $(2\pi f)^2 P_x(f)$
• State and prove the sampling theorem for bandlimited WSS processes
• Derive the Karhunen-Loève expansion and explain its optimality as a basis expansion
• Connect the KL expansion to PCA and MIMO channel decomposition