Efficient Computation of the Fourier Transform on Finite Groups
Efficient Computation of the Fourier Transform on Finite Groups
Let $G$ be a finite group, $f:G \to {\mathbf {C}}$ a function, and $\rho$ an irreducible representation of $G$. The Fourier transform is defined as $\hat f(\rho ) = {\Sigma _{s \in G}}f(s)\rho (s)$. Direct computation for all irreducible representations involves order ${\left | G \right |^2}$ operations. We derive …