Demystification of the geometric Fourier transforms and resulting convolution theorems. (3rd September 2015)

• Record Type: Journal Article
• Authors: Bujack, Roxana; Scheuermann, Gerik; Hitzer, Eckhard
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 7(2016:May 15)
• Page Start: 1877
• Page End: 1890
• Publication Date: 2015-09-03
• Subjects: geometric algebra -- Clifford algebra -- Fourier transform -- trigonometric transform -- convolution theorem; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3607
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.