Signals and Systems I: Fourier Transform and Spectral Analysis

This lecture covers topics related to signals and systems, including Fourier series, average energy calculation, Parseval relations, functional spaces, cross-correlation spectra, autocorrelation function, spectral density, and energy in a frequency band. It also discusses the properties of signals with finite energies, symmetrization of theory, and simplification of convergence conditions. The lecture emphasizes the importance of understanding autocorrelation functions, cross-correlation spectra, and the Parseval relation in both periodic and real cases.