Convolution Theorems for Quaternion Fourier Transform: Properties and Applications | Zendy

Mawardi Bahri | Zendy; Ryuichi Ashino | Zendy; Rémi Vaillancourt | Zendy

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Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

Author(s) -

Mawardi Bahri,

Ryuichi Ashino,

Rémi Vaillancourt

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/162769

Subject(s) - mathematics , quaternion , convolution (computer science) , convolution theorem , fourier transform , algebra over a field , convolution power , fourier inversion theorem , pure mathematics , mathematical analysis , fourier analysis , fractional fourier transform , geometry , computer science , machine learning , artificial neural network

General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework

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