Analysis and Synthesis of Deterministic Signals

This lecture covers the vectorial representation of signals, projection theorem, development in series of orthogonal functions, Gram-Schmidt orthogonalization, and examples of orthogonal functions. It explains how signals can be represented as vectors in a space defined by a basis, the relationship between scalar product and distance, and the series expansion for calculating coefficients. The projection theorem is discussed, showing how to minimize the distance between a signal and its approximation. The lecture also explores the Gram-Schmidt orthogonalization process and examples of orthogonal functions like shifted rectangles, sinusoids, and Fourier series.