37

Periodic Functions and Regular Arrays

In this chapter, we will tie together several different threads of Fourier analysis. We will extend our discussion from part II regarding periodic functions and their Fourier series, and, using our generalized theory, we will discover the intimate relation between the Fourier series and the Fourier transforms of periodic functions. In addition, we will develop material that will help form the framework for yet another “theory” of Fourier analysis — the “discrete theory” — which will be developed in later chapters.

37.1  Periodic Generalized Functions

Basics

When we say a generalized function f is periodic (in the generalized sense), we mean there is a positive value p such that, as generalized functions, ...

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