The unified theory of n-dimensional complex and hypercomplex analytic signals

• Autorzy: Hahn S. , Snopek K.
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the theory of n-D complex and hypercomplex analytic signals with emphasis on the 3-dimensional (3-D) case. Their definitions are based on the proposed general n-D form of the Cauchy integral. The definitions are presented in signaland frequency domains. The new notion of lower rank signals is introduced. It is shown that starting with the 3-D analytic hypercomplex signals and decreasing their rank by extending the support in the frequency-space to a so called space quadrant, we get a signal having the quaternionic structure. The advantage of this procedure is demonstrated in the context of the polar representation of 3-D hypercomplex signals. Some new reconstruction formulas are presented. Their validation has been confirmed using two 3-D test signals: a Gaussian one and a spherical one.

Słowa kluczowe

EN

complex/hypercomplex analytic signal; hypercomplex Fourier transform; hypercomplex delta distribution

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2011
• Tom: Vol. 59, nr 2
• Strony: 167--181
• Opis fizyczny: Bibliogr. 30 poz., rys., tab.

Twórcy

autor

Hahn S.

autor

Snopek K.

• Institute of Radioelectronics, Warsaw University of Technology, 15/19 Nowowiejska St., 00-665 Warszawa, Poland,

Bibliografia

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