Windowed Fourier transform of two-dimensional quaternionic signals

被引：48

作者：

Bahri, Mawardi ^{[2
]}

Hitzer, Eckhard S. M. ^{[3
]}

Ashino, Ryuichi ^{[4
]}

Vaillancourt, Remi ^{[1
]}

机构：

[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

[2] Hasanuddin Univ, Dept Math, Tamalanrea Makassar, Indonesia

[3] Univ Fukui, Dept Appl Phys, Fukui 9108507, Japan

[4] Osaka Kyoiku Univ, Div Math Sci, Osaka 5828582, Japan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 216卷 / 08期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Quaternionic Fourier transform; Quaternionic windowed Fourier transform; Signal processing; Heisenberg type uncertainty principle; PRINCIPLES; FIELDS;

D O I：

10.1016/j.amc.2010.03.082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternion-valued 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. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2366 / 2379

页数：14

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