The Scientist and Engineer's Guide to
Digital Signal Processing
By Steven W. Smith, Ph.D.

Chapter 11: Fourier Transform Pairs

For every time domain waveform there is a corresponding frequency domain waveform, and vice versa. For example, a rectangular pulse in the time domain coincides with a sinc function [i.e., sin(x)/x] in the frequency domain. Duality provides that the reverse is also true; a rectangular pulse in the frequency domain matches a sinc function in the time domain. Waveforms that correspond to each other in this manner are called Fourier transform pairs. Several common pairs are presented in this chapter.

• Delta Function Pairs
• The Sinc Function
• Other Transform Pairs
• Gibbs Effect
• Harmonics
• Chirp Signals