B. Mawardi, E. Hitzer, A. Hayashi, R. Ashino
An Uncertainty Principle for Quaternion Fourier Transform
Computer & Mathematics with Applications, Vol. 56, pp. 2398-2410 (2008).

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.

Keywords: Quaternion algebra, Quaternionic Fourier transform, Uncertainty principle, Gaussian quaternion signal, Hypercomplex functions

Mathematical Subject Classicfication (1991): 30G35, 42B10, 94A12, 11R52

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