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Proceedings Paper

Cross Hilbert time-frequency distributions
Author(s): William J. Williams
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Paper Abstract

It is mathematically convenient to consider both positive nd negative frequencies in signal representation. This idea is critically important to time-frequency analysis. Usually, however one is presented with real signals. It is also well known that the analytic signal is formed using the Hilbert transform. Some interesting and potentially useful relationships are developed for a signal and its Hilbert transform. Some interesting and potentially useful relationships are developed for a signal and its Hilbert transform in this paper. Cross-Hilbert time-frequency distributions (TFDs) between a signal and its Hilbert transform. The relationships between TFDs of signals and cross-Hilbert TFDs of signals are examined. It is shown how interactions between these TFDs yield results which are confined to either the positive or negative frequency planes. Some results which may seem counterintuitive are pointed out. Finally, some interesting results which use the concepts developed for separation of mixed signals by manipulating the associated TFDs are presented.

Paper Details

Date Published: 2 October 1998
PDF: 10 pages
Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); doi: 10.1117/12.325673
Show Author Affiliations
William J. Williams, Univ. of Michigan (United States)


Published in SPIE Proceedings Vol. 3461:
Advanced Signal Processing Algorithms, Architectures, and Implementations VIII
Franklin T. Luk, Editor(s)

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