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2010

Windowed Fourier transform of two-dimensional quaternionic signals

10 years 4 months ago
Windowed Fourier transform of two-dimensional quaternionic signals
In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternionvalued signals, called the quaternionic windowed Fourier transform (QWFT). Using the spectral representation of the quaternionic Fourier transform (QFT), we derive several important properties such as reconstruction formula, reproducing kernel, isometry, and orthogonality relation. Taking the Gaussian function as window function we obtain quaternionic Gabor filters which play the role of coefficient functions when decomposing the signal in the quaternionic Gabor basis. We apply the QWFT properties and the (right-sided) QFT to establish a Heisenberg type uncertainty principle for the QWFT. Finally, we briefly introduce an application of the QWFT to a linear time-varying system. Keywords : quaternionic Fourier transform, quaternionic windowed Fourier transform, signal processing, Heisenberg type uncertainty principle
Mawardi Bahri, Eckhard S. M. Hitzer, Ryuichi Ashin
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2010
Where AMC
Authors Mawardi Bahri, Eckhard S. M. Hitzer, Ryuichi Ashino, Rémi Vaillancourt
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