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Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case
The construction of Gabor's (1946) complex signal-which is also known as the analytic signal-provides direct access to a real one-dimensional (1-D) signal's local amplitude and phase. The complex signal is built from a real signal by adding its Hilbert transform-which is a phase-shifted ve...
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Published in: | IEEE transactions on signal processing 2001-11, Vol.49 (11), p.2844-2852 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | The construction of Gabor's (1946) complex signal-which is also known as the analytic signal-provides direct access to a real one-dimensional (1-D) signal's local amplitude and phase. The complex signal is built from a real signal by adding its Hilbert transform-which is a phase-shifted version of the signal-as an imaginary part to the signal. Since its introduction, the complex signal has become an important tool in signal processing, with applications, for example, in narrowband communication. Different approaches to an n-D analytic or complex signal have been proposed in the past. We review these approaches and propose the hypercomplex signal as a novel extension of the complex signal to n-D. This extension leads to a new definition of local phase, which reveals information on the intrinsic dimensionality of the signal. The different approaches are unified by expressing all of them as combinations of the signal and its partial and total Hilbert transforms. Examples that clarify how the approaches differ in their definitions of local phase and amplitude are shown. An example is provided for the two-dimensional (2-D) hypercomplex signal, which shows how the novel phase concept can be used in texture segmentation. |
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ISSN: | 1053-587X 1941-0476 |
DOI: | 10.1109/78.960432 |