Difference between revisions of "Fourier transformation"

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