Browsing by Author "Michel, Olivier"

Now showing 1 - 4 of 4
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    Measuring Time-Frequency Information and Complexity using the Renyi Entropies
    (1995-09-01) Baraniuk, Richard G.; Flandrin, Patrick; Michel, Olivier; Digital Signal Processing (http://dsp.rice.edu/)
    In search of a nonparametric indicator of deterministic signal complexity, we link the Renyi entropies to time-frequency representations. The resulting measures show promise in several situations where concepts like the time-bandwidth product fail.
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    Measuring Time-Frequency Information Content using the Renyi Entropies
    (2001-05-01) Baraniuk, Richard G.; Flandrin, Patrick; Janssen, A. J. E. M.; Michel, Olivier; Digital Signal Processing (http://dsp.rice.edu/)
    The generalized entropies of Renyi inspire new measures for estimating signal information and complexity in the time-frequency plane. When applied to a time-frequency representation (TFR) from Cohen's class or the affine class, the Renyi entropies conform closely to the notion of complexity that we use when visually inspecting time-frequency images. These measures possess several additional interesting and useful properties, such as accounting and cross-component and transformation invariances, that make them natural for time-frequency analysis. This paper comprises a detailed study of the properties and several potential applications of the Renyi entropies, with emphasis on the mathematical foundations for quadratic TFRs. In particular, for the Wigner distribution, we establish that there exist signals for which the measures are not well defined.
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    Time-Frequency Complexity and Information
    (1994-04-01) Flandrin, Patrick; Baraniuk, Richard G.; Michel, Olivier; Digital Signal Processing (http://dsp.rice.edu/)
    Many functions have been proposed for estimating signal information content and complexity on the time-frequency plane, including moment-based measures such as the time-bandwidth product and the Shannon and Renyi entropies. When applied to a time-frequency representation from Cohen's class, the Renyi entropy conforms closely to the visually based notion of complexity that we use when inspecting time-frequency images. A detailed discussion reveals many of the desirable properties of the Renyi information measure for both deterministic and random signals.
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    Time-Frequency Based Distance and Divergence Measures
    (1994-10-01) Michel, Olivier; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    A study of the phase and amplitude sensitivity of the recently proposed Renyi time-frequency information measure leads to the introduction of a new "Jensen-like" divergence measure. While this quantity promises to be a useful indicator of the distance between two time-frequency distributions, it is limited to the analysis of positive definite TFDs. In spite of this rather severe limitation, this measure could prove useful for time-frequency based detection. We illustrate with an example of detecting a signal in additive noise.