ISSN:
1573-0824
Keywords:
Gram-Charlier Series
;
Edgeworth Series
;
probability theory
;
time-frequency analysis
;
characteristic function
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008454223082
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