The Study of Properties of n-D Analytic Signals and Their Spectra in Complex and Hypercomplex Domains

Snopek, Kajetana Marta

The Study of Properties of n-D Analytic Signals and Their Spectra in Complex and Hypercomplex Domains

Files

12_01_0029_0036.pdf(8.12 MB)

Date

2012-04

Authors

Snopek, Kajetana Marta

Publisher

Společnost pro radioelektronické inženýrství

Abstract

In the paper, two various representations of a n-dimensional (n-D) real signal u(x1,x2,…,xn) are investigated. The first one is the n-D complex analytic signal with a single-orthant spectrum defined by Hahn in 1992 as the extension of the 1-D Gabor’s analytic signal. It is compared with two hypercomplex approaches: the known n-D Clifford analytic signal and the Cayley-Dickson analytic signal defined by the Author in 2009. The signal-domain and frequency-domain definitions of these signals are presented and compared in 2-D and 3-D. Some new relations between the spectra in 2-D and 3-D hypercomplex domains are presented. The paper is illustrated with the example of a 2-D separable Cauchy pulse.

Keywords

Analytic signals, Cayley-Dickson algebra, Clifford algebra, Clifford Fourier transform, Quaternion Fourier transform, Octonion Fourier transform

Citation

Radioengineering. 2012, vol. 21, č. 1, s. 29-36. ISSN 1210-2512
http://www.radioeng.cz/fulltexts/2012/12_01_0029_0036.pdf

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution 3.0 Unported License
http://creativecommons.org/licenses/by/3.0/