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

[ PDF ] 428K

[Geometric Calculus Japan index]