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arXiv · 1303.1752

Convolution products for hypercomplex Fourier transforms

Roxana Bujack·Hendrik De Bie·Nele De Schepper·Gerik Scheuermann
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Abstract

Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the Fourier domain, is the lack of a proper convolution theorem. The present paper develops and studies two conceptually new ways to define convolution products for such transforms. As a by-product, convolution theorems are obtained that will enable the development and fast implementation of new filters for quaternionic signals and systems, as well as for their higher dimensional counterparts.

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Roxana Bujack, Hendrik De Bie, Nele De Schepper, Gerik Scheuermann. 2013-03-07. Convolution products for hypercomplex Fourier transforms. https://arxiv.org/abs/1303.1752

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