Cross Hilbert time-frequency distributions

William J. Williams

doi:10.1117/12.325673

2 October 1998 Cross Hilbert time-frequency distributions

William J. Williams

Proceedings Volume 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII; (1998) https://doi.org/10.1117/12.325673
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

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.

Citation Download Citation

William J. Williams "Cross Hilbert time-frequency distributions", Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); https://doi.org/10.1117/12.325673

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