Algorithms for Periodic Functions

In this chapter we show how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm, including not-so special case situations such as when the data to be transformed are real. In those situations, we speed up the transforms by about a factor of two by exploiting symmetries in the data and the coefficients. We end this chapter by showing how to approximate the derivatives of periodic functions, which are the fundamental approximations that we need to solve partial differential equations with periodic boundary conditions.