Title: A Generalized Poisson Summation Formula and its Application to Fast Linear Convolution
Abstract: In this letter, 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 present 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. Other techniques that achieve this have been introduced in the past using different approaches. The newly proposed theory however, constitutes a unifying framework to the methods previously published.
Publication Year: 2011
Publication Date: 2011-09-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 12
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