Fourier Series and Transforms: Introduction and Properties

This lecture introduces the concepts of Fourier series and Fourier transforms, explaining how any periodic function can be decomposed into sines and cosines. It covers the properties of these transforms, including linearity, translation, modulation, and scaling. The lecture also discusses the convolution operation in both time and frequency domains, highlighting its commutativity, associativity, and distributivity properties. The Discrete Fourier Transform (DFT) is presented as a discretized version of the Fourier transform, suitable for computer implementation. Examples and demonstrations using Matlab are provided to illustrate these concepts.