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.
CHAPTER
Fourier Transform Pairs
11

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
For discrete signals, the delta function is a simple waveform, and has an
equally simple Fourier transform pair. Figure 11-1a shows a delta function in