ABSTRACT
Fourier series and Fourier transforms are of fundamental importance for the mathematical theory of signals. We will discuss both continuous and discrete cases of Fourier series in this chapter. The continuous case is very well known and can be found in many textbooks on integral transforms and boundary value problems of partial differential equations. The convergence of Fourier series is discussed, and Heaviside unit step function, Dirac δ-function, Dirichlet kernel, and Gibbs phenomenon are presented. The discrete case related to signals and filters is discussed in detail in Chapter 4.
