Convolution products for hypercomplex Fourier transforms
Classical Analysis and ODEs
2013-03-08 v1
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.
Keywords
Cite
@article{arxiv.1303.1752,
title = {Convolution products for hypercomplex Fourier transforms},
author = {Roxana Bujack and Hendrik De Bie and Nele De Schepper and Gerik Scheuermann},
journal= {arXiv preprint arXiv:1303.1752},
year = {2013}
}
Comments
18 pages, two columns, accepted in J. Math. Imaging Vision