Principles of Fourier Analysis, 2nd Edition

5

Symmetry and Periodicity

In this chapter, we will review some basic facts regarding functions whose graphs exhibit some sort of repetitive pattern. Either the graphs are symmetric or antisymmetric about the origin (even and odd functions), or they continually repeat themselves at regular intervals along the real line (periodic functions). We are interested in even and odd functions because, on occasion, we will exploit the properties discussed here to simplify our work. Our main interest, however, will be with periodic functions because of the central role these functions will play in our work.

5.1    Even and Odd Functions

Let f be a function defined on a symmetric interval (−α, α) for some α > 0. The function is said to be an even function ...