Encyclopedia  |   World Factbook  |   World Flags  |   Reference Tables  |   List of Lists     
   Academic Disciplines  |   Historical Timeline  |   Themed Timelines  |   Biographies  |   How-Tos     
Sponsor by The Tattoo Collection
List of Fourier-related transforms
Main Page | See live article | Alphabetical index

List of Fourier-related transforms

This is a list of linear transformations of functionss related to the Fourier transform. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component.

Applied to functions of continuous arguments, Fourier-related transforms include:

For usage on computers, discrete arguments (e.g. functions of a series of discrete samples) are more appropriate, and are handled by the transforms (analogous to the continuous cases above):

The usage of all of these transforms is greatly facilitated by the existence of efficient algorithms based on a fast Fourier transform (FFT). The Nyquist-Shannon sampling theorem is critical for understanding the output of such discrete transforms.

See also