- Tytuł:
- The unified theory of n-dimensional complex and hypercomplex analytic signals
- Autorzy:
-
Hahn, S.
Snopek, K. - Powiązania:
- https://bibliotekanauki.pl/articles/202287.pdf
- Data publikacji:
- 2011
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
complex/hypercomplex analytic signal
hypercomplex Fourier transform
hypercomplex delta distribution - Opis:
- 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.
- Źródło:
-
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2011, 59, 2; 167-181
0239-7528 - Pojawia się w:
- Bulletin of the Polish Academy of Sciences. Technical Sciences
- Dostawca treści:
- Biblioteka Nauki
Artykuł