Fourier transform on finite groups

In mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. == Definitions == The Fourier transform of a function f : G → C {\displaystyle f:G\to \mathbb {C} } at a representation ϱ : G → G L d ϱ ( C ) {\displaystyle \varrho :G\to \mathrm {GL} _{d_{\varrho }}(\mathbb {C} )} of G {\displaystyle G} is f ^ ( ϱ ) = ∑ a ∈ G f ( a ) ϱ ( a ) .

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