# Fourier transformation

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Fourier transformation is an invertible integral transformation that decompose a square integrable, piecewise continuous function 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.