# Difference between revisions of "Fourier transformation"

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− | Fourier transformation is an invertible integral transformation that decompose a square integrable, [[piecewise continuous | + | Fourier transformation is an invertible integral transformation that decompose a square integrable, [[piecewise continuous functions ]] on a [[topological group]] into a linear combination of basis elements. |

Often, functions which are difficult to analyze in one topological group become much easier to analyze when transformed to another topological group. | Often, functions which are difficult to analyze in one topological group become much easier to analyze when transformed to another topological group. |

## Revision as of 01:58, 24 March 2007

Fourier transformation is an invertible integral transformation that decompose a square integrable, piecewise continuous functions on a topological group into a linear combination of basis elements.

Often, functions which are difficult to analyze in one topological group become much easier to analyze when transformed to another topological group.

## Discrete Fourier transformation

Discrete Fourier transformations are defined on discrete topological groups, and the integral is replaced by summation.