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Fast complexified quaternion Fourier transform

Said, S and Le Bihan, N and Sangwine, SJ (2008) 'Fast complexified quaternion Fourier transform.' IEEE Transactions on Signal Processing, 56 (4). 1522 - 1531. ISSN 1053-587X

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Abstract

In this paper, we consider the extension of the Fourier transform to biquaternion-valued signals. We introduce a transform that we call the biquaternion Fourier transform (BiQFT). After giving some general properties of this transform, we show how it can be used to generalize the notion of analytic signal to complex-valued signals. We introduce the notion of hyperanalytic signal. We also study the Hermitian symmetries of the BiQFT and their relation to the geometric nature of a biquaternion-valued signal. Finally, we present a fast algorithm for the computation of the BiQFT. This algorithm is based on a (complex) change of basis and four standard complex FFTs. © 2008 IEEE.

Item Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 05 Mar 2013 14:05
Last Modified: 30 Jan 2019 16:16
URI: http://repository.essex.ac.uk/id/eprint/5557

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