Signals & Systems I: Cross-Correlation and Convolution

This lecture covers the definition of cross-correlation function and dot product for complex finite energy signals, intercorrelation between signals, reversal operators, optimal detector in the presence of white noise, and signal detection. It also discusses cross-correlation in sonar, change of base in the plan, least squares approximation, signal approximation, orthonormal system of functions, Hilbert spaces, orthogonality, similarity, orthonormal families of functions, and proof of the orthogonal approximation theorem.