Principles of Fourier Analysis, 2nd Edition

39

Periodic, Regular Arrays

In earlier chapters, we computed Fourier transforms of periodic functions (obtaining regular arrays of delta functions) and Fourier transforms of regular arrays (obtaining periodic functions). You may have even computed a Fourier transform or Fourier series for one or two regular arrays that were also periodic (such as a comb function). In this chapter we will look more closely at the computation of transforms of those delta function arrays that are both periodic and regular. In the process, we will obtain results and formulas that will be particularly useful in developing the “discrete theory” of Fourier analysis in the next chapter.

39.1  The Index Period and Other Basic Notions

Let us consider an arbitrary periodic, ...