A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals
P.J. Schreier, L.L. Scharf, A. Hanssen, in: Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory, 2005, pp. 966–969.
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Schreier, Peter J.;
Scharf, Louis L.;
Hanssen, Alfred
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Abstract
Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek distribution is a time- and frequency-shift covariant, bilinear time-frequency distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek distribution. We propose to construct estimators of the Rihaczek distribution using a factored kernel in Cohen’s class of bilinear time-frequency distributions
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Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory
Page
966–969
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Schreier PJ, Scharf LL, Hanssen A. A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals. In: Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory. ; 2005:966–969. doi:10.1109/ISIT.2005.1523481
Schreier, P. J., Scharf, L. L., & Hanssen, A. (2005). A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals. Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory, 966–969. https://doi.org/10.1109/ISIT.2005.1523481
@inproceedings{Schreier_Scharf_Hanssen_2005, title={A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals}, DOI={10.1109/ISIT.2005.1523481}, booktitle={Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory}, author={Schreier, Peter J. and Scharf, Louis L. and Hanssen, Alfred}, year={2005}, pages={966–969} }
Schreier, Peter J., Louis L. Scharf, and Alfred Hanssen. “A Geometric Interpretation of the Rihaczek Time-Frequency Distribution for Stochastic Signals.” In Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory, 966–969, 2005. https://doi.org/10.1109/ISIT.2005.1523481.
P. J. Schreier, L. L. Scharf, and A. Hanssen, “A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals,” in Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory, 2005, pp. 966–969, doi: 10.1109/ISIT.2005.1523481.
Schreier, Peter J., et al. “A Geometric Interpretation of the Rihaczek Time-Frequency Distribution for Stochastic Signals.” Proc.\ IEEE Int.\ Symp.\ Inform.\ Theory, 2005, pp. 966–969, doi:10.1109/ISIT.2005.1523481.
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