POLISH ACADEMY of SCIENCES
TECHNICAL SCIENCES
| BULLETIN
of the
POLISH ACADEMY of SCIENCES TECHNICAL SCIENCES |
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| Volume
59, Issue 2, June 2011
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| Aims&Scope, Subscription | Editors | Authors' guide | to read PDF files | mirror: http://fluid.ippt.gov.pl/~bulletin/ |
| pp 167 - 181 |
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The unified theory of n-dimensional complex and hypercomplex analytic signals |
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| S.L. HAHN and K.M. SNOPEK |
| 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. |
| Key words: |
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complex/hypercomplex analytic signal, hypercomplex Fourier transform, hypercomplex delta distribution |
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| Issue Index | Authors Index | Scope Index | Web Info |
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| Aims&Scope, Subscription | Editors | Authors' guide | to read PDF files |
| Copyright ® Bulletin of the Polish Academy of Sciences: Technical Sciences |
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