Generalization of the Gram-Charlier/Edgeworth Series and Application to Time-Frequency Analysis |
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Authors: | Cohen Leon |
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Affiliation: | (1) Hunter College and Graduate Center of CUNY, 695 Park Ave., New York, NY 10021, USA |
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Abstract: | We derive a general equation relating probability densities and as special cases we the obtain Gram-Charlier and Edgeworth series. This allows us to generalize these methods and clarify a number of issues pertaining to both probability theory and time-frequency analysis. In particular we show how the Gram-Charlier and Edgeworth series are related to the kernel method of time-frequency analysis. The approach allows us to construct densities that satisfy given constraints such as joint moments or conditional moments. Also, we show that the kernel has to be signal dependent and that to obtain a proper distribution it should be the ratio of two characteristic functions. |
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Keywords: | Gram-Charlier Series Edgeworth Series probability theory time-frequency analysis characteristic function |
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