Authors: Mawardi Bahri, Eckhard Hitzer, Akihisa Hayashi, Ryuichi Ashino
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. Key words: Quaternion algebra, Quaternionic Fourier transform, Uncertainty principle, Gaussian quaternion signal, Hypercomplex functions Math. Subj. Class.: 30G35, 42B10, 94A12, 11R52
Comments: 20 Pages. Computer & Mathematics with Applications, 56, pp. 2398-2410 (2008). DOI: 10.1016/j.camwa.2008.05.032, 3 figures, 1 table.
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