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.
- 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
|Modified:||18 August 2017|
|Authors:||Jorge Martinez, Richard Heusdens, Richard Hendriks|