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Quaternion Fourier and linear canonical inversion theorems
Author(s) -
Hu XiaoXiao,
Kou Kit Ian
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4148
Subject(s) - quaternion , mathematics , fourier transform , fourier inversion theorem , fractional fourier transform , inversion (geology) , mathematical analysis , fourier series , pure mathematics , discrete fourier transform (general) , fourier analysis , geometry , structural basin , paleontology , biology
The quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In addition, understanding the QFT paves the way for understanding other integral transform, such as the quaternion fractional Fourier transform, quaternion linear canonical transform, and quaternion Wigner–Ville distribution. The aim of this paper is twofold: first to provide some of the theoretical background regarding the quaternion bound variation function. We then apply it to derive the quaternion Fourier and linear canonical inversion formulas. Secondly, to provide some in tuition for how the quaternion Fourier and linear canonical inversion theorems work on the absolutely integrable function space. Copyright © 2016 John Wiley & Sons, Ltd.