The Study of Properties of n-D Analytic Signals and Their Spectra in Complex and Hypercomplex Domains
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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.
KeywordsAnalytic signals, Cayley-Dickson algebra, Clifford algebra, Clifford Fourier transform, Quaternion Fourier transform, Octonion Fourier transform
Document typePeer reviewed
Document versionFinal PDF
SourceRadioengineering. 2012, vol. 21, č. 1, s. 29-36. ISSN 1210-2512
- 2012/1