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Demystification of the geometric Fourier transforms and resulting convolution theorems
Author(s) -
Bujack Roxana,
Scheuermann Gerik,
Hitzer Eckhard
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.3607
Subject(s) - convolution (computer science) , mathematics , interpretation (philosophy) , separable space , constant (computer programming) , fourier transform , convolution theorem , sine and cosine transforms , algebra over a field , pure mathematics , mathematical analysis , fourier analysis , fractional fourier transform , computer science , artificial intelligence , artificial neural network , programming language
T. Qian As it will turn out in this paper, the recent hype about most of the Clifford–Fourier transforms is not thoroughly worth the pain. Almost everyone that has a real application is separable, and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial. Copyright © 2015 John Wiley & Sons, Ltd.