Generalized discrete Fourier transform (gDFT)
In the corresponding paper, a generalized Fourier transform is introduced and its corresponding generalized Poisson summation formula is derived.
For discrete, Fourier based, signal processing, this formula shows that a special form of control on the periodic repetitions that occur due to sampling in the reciprocal domain is possible.
The paper is focused on the derivation and analysis of a weighted circular convolution theorem. We use this specific result to compute linear convolutions in the generalized Fourier domain, without the need of zero-padding. This results in faster, more resource- efficient computations.