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.

Related publications

  1. A Generalized Poisson Summation Formula and its Application to Fast Linear Convolution
    J. Martinez; R. Heusdens; R.C. Hendriks;
    IEEE Signal Process. Lett.,
    Volume 18, Issue 9, pp. 501-504, 2011. DOI: 10.1109/LSP.2011.2161078} project = {audio
    document

Source: xkcd.com

Repository data

File: GDFT_functions.zip
Size: 6 kB
Modified: 18 August 2017
Type: software
Authors: Jorge Martinez, Richard Heusdens, Richard Hendriks
Date: January 2011
Contact: Richard Hendriks