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Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis

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Quaternion and Clifford Fourier Transforms and Wavelets

Part of the book series: Trends in Mathematics ((TM))

Abstract

Quaternion Fourier transforms (QFT’s) provide expressive power and elegance in the analysis of higher-dimensional linear invariant systems. But, this power comes at a cost – an overwhelming number of choices in the QFT definition, each with consequences. This chapter explores the evolution of QFT definitions as a framework from which to solve specific problems in vector-image and vector-signal processing.

‘Did you ask a good question today?’ – Janet Teig

Mathematics Subject Classification (2010). Primary 11R52; secondary 42B10.

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References

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Author information

Authors and Affiliations

  1. Engineering Fellow Goodrich, Sensors and Integrated Systems, 14300 Judicial Road, Burnsville, MN, 55306, USA

    Todd Anthony Ell

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  1. Todd Anthony Ell
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Correspondence to Todd Anthony Ell .

Editor information

Editors and Affiliations

  1. , Department of Material Science, International Christian University, Osawa 3-10-2Mitaka-shi, Tokyo, 181-8585, Japan

    Eckhard Hitzer

  2. School of Computer Science and, Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom

    Stephen J. Sangwine

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Ell, T.A. (2013). Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis. In: Hitzer, E., Sangwine, S. (eds) Quaternion and Clifford Fourier Transforms and Wavelets. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0603-9_1

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