Abstract
The quaternionic Fourier transform (QFT) plays a vital role in the representation of signals and transforms a quaternionic 2 D signal into a quaternion-valued frequency domain signal. Associated with a kind of phase functions satisfying certain assumption, this paper generalizes the QFT to a kind of non-harmonic quaternionic Fourier transform (NQFT) and derives several important properties such as the scalar Plancherel and Parseval theorems, partial derivative, specific shift. The uncertainty principle for QFT is generalized for the NQFT. It is shown that only a Gaussian-type quaternion signal minimizes the uncertainty.
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