Fourier Analysis

Abstract

The frequency domain plays a central role in our discussion and analysis throughout this book. It is thus appropriate to begin with a treatment of Fourier theory. There are four basic Fourier transforms. These are:

• (i) Fourier series that map periodic continuous-time functions into sequences in the frequency domain;

• (ii) continuous-time Fourier transforms that map continuous-time functions into continuous frequency domain functions;

• (iii) discrete-time Fourier transforms (DTFT) that map time domain sequences into periodic continuous frequency domain functions;

• (iv) discrete Fourier transforms (DFT) that map periodic sequences in the time domain to periodic sequences in the frequency domain.