Discrete Fourier Transform

Abstract

Nowadays most of the time when you take the Fourier transform it will be using a digital processor—either on the computer, on your phone, or some other device. You are actually evaluating the discrete Fourier transform. Much of what we have already discussed about the continuous Fourier transform carries over to the Discrete Fourier transform so this module will be relatively short. We will begin by developing the discrete time Fourier transform (DTFT) which maps a discrete sequence from the time domain to a continuous transform in the frequency domain. From this we will develop the discrete Fourier transform (DFT) which takes a discrete sequence in the time domain to a discrete sequence in the frequency domain.