# Generalized discrete Fourier transform (gDFT)

**Topic:**General signal processing

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

**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

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### Repository data

File: | GDFT_functions.zip |
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Size: | 6 kB |

Modified: | 18 August 2017 |

Type: | software |

Authors: | Jorge Martinez, Richard Heusdens, Richard Hendriks |

Date: | January 2011 |

Contact: | Richard Hendriks |