A New Interpretation of Bilinear Time-Frequency Distributions
P.J. Schreier, in: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 2007, pp. 1133–1136.
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Author
Schreier, Peter J.
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Abstract
Wigner’s theorem states that there exists no bilinear time-frequency distribution (TFD) that has correct marginals and is nonnegative everywhere. This means that any attempt to interpret a bilinear TFD as an energy or power distribution must be fraught with problems. In this paper, an alternative perspective is proposed, which allows a local interpretation at a point in the time-frequency plane. This approach is based on analyzing the properties of a chirping ellipse that, at a given time instant, gives the best local approximation of the signal from a given frequency. This chirping ellipse is described in terms of its mean shape, orientation, and direction of polarization (counterclockwise or clockwise). A time-frequency coherence measures the quality of the approximation that this ellipse presents. The ellipse parameters and the time-frequency coherence can be expressed in terms of the Rihaczek TFD
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Proceedings Title
Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.
Volume
3
Page
1133–1136
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Schreier PJ. A New Interpretation of Bilinear Time-Frequency Distributions. In: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process. Vol 3. ; 2007:1133–1136. doi:10.1109/ICASSP.2007.366884
Schreier, P. J. (2007). A New Interpretation of Bilinear Time-Frequency Distributions. Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 3, 1133–1136. https://doi.org/10.1109/ICASSP.2007.366884
@inproceedings{Schreier_2007, title={A New Interpretation of Bilinear Time-Frequency Distributions}, volume={3}, DOI={10.1109/ICASSP.2007.366884}, booktitle={Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.}, author={Schreier, Peter J.}, year={2007}, pages={1133–1136} }
Schreier, Peter J. “A New Interpretation of Bilinear Time-Frequency Distributions.” In Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 3:1133–1136, 2007. https://doi.org/10.1109/ICASSP.2007.366884.
P. J. Schreier, “A New Interpretation of Bilinear Time-Frequency Distributions,” in Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 2007, vol. 3, pp. 1133–1136, doi: 10.1109/ICASSP.2007.366884.
Schreier, Peter J. “A New Interpretation of Bilinear Time-Frequency Distributions.” Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., vol. 3, 2007, pp. 1133–1136, doi:10.1109/ICASSP.2007.366884.
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