Editing Discrete Fourier transform (section)

=== Other finite groups ===
{{Main|Fourier transform on finite groups}}
The standard DFT acts on a sequence ''x''<sub>0</sub>, ''x''<sub>1</sub>, ..., ''x''<sub>''N''−1</sub> of complex numbers, which can be viewed as a function {0, 1, ..., ''N'' − 1} → '''C'''. The multidimensional DFT acts on multidimensional sequences, which can be viewed as functions
:<math> \{0, 1, \ldots, N_1-1\} \times \cdots \times \{0, 1, \ldots, N_d-1\} \to \mathbb{C}. </math>
This suggests the generalization to [[Fourier transform on finite groups|Fourier transforms on arbitrary finite groups]], which act on functions ''G'' → '''C''' where ''G'' is a [[finite group]]. In this framework, the standard DFT is seen as the Fourier transform on a [[cyclic group]], while the multidimensional DFT is a Fourier transform on a direct sum of cyclic groups.

Further, Fourier transform can be on cosets of a group.