Fourier Analysis and the Discrete Fourier Transform

Abstract

Having discussed sampling and time-limiting and how they affect a signal’s spectrum, we move on to the estimation of the spectrum of a signal from the signal’s samples. In this chapter, we introduce the discrete Fourier transform, we discuss its significance, and we derive its properties. Then we discuss the family of algorithms know as fast Fourier transforms. We explain their significance, describe how one uses them, and discuss zero-padding and the fast convolution algorithm.