Chapter 14: Power Spectral Density

Learning Objectives

• State and prove the Wiener-Khinchin theorem for both discrete-time and continuous-time WSS processes
• Explain why the PSD is real, non-negative, and even for real-valued processes, and relate total power to the integral of the PSD
• Define white noise via its flat PSD, compute band-limited white noise autocorrelation, and explain why infinite-bandwidth white noise is an idealization
• Derive the cross-spectral density and the input-output PSD relation for LTI systems
• Compute the discrete-time PSD via the DTFT of the autocorrelation and understand the periodogram as a finite-data estimator
• Apply PSD analysis to characterize noise in communication receivers and design matched filters