An uncertainty principle for quaternion Fourier transform

Authors:
Mawardi Bahri;Eckhard S. M. Hitzer;Akihisa Hayashi;Ryuichi Ashino
Affiliations:
Department of Applied Physics, University of Fukui, Fukui 910-8507, Japan;Department of Applied Physics, University of Fukui, Fukui 910-8507, Japan;Department of Applied Physics, University of Fukui, Fukui 910-8507, Japan;Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japan
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty.