Continuous quaternion fourier and wavelet transforms-Reference-Cited by-同舟云学术

Continuous quaternion fourier and wavelet transforms

Published:2014-07 Issue:04 Volume:12 Page:1460003
ISSN:0219-6913
Container-title:International Journal of Wavelets, Multiresolution and Information Processing
language:en
Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.

Author:

Bahri Mawardi¹,Ashino Ryuichi²,Vaillancourt Rémi³

Affiliation:

1. Department of Mathematics, Universitas Hasanuddin, Makassar 90245, Indonesia

2. Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japan

3. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5, Canada

Abstract

A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel [Formula: see text] is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219691314600030

Reference24 articles.

1. Local quaternion Fourier transform and color image texture analysis

2. Clifford Algebra-Valued Wavelet Transform on Multivector Fields

3. Two-dimensional quaternion wavelet transform

4. Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl3,0

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