Instantaneous frequency estimation using stochastic calculus and bootstrapping

Authors:
A. Abutaleb
Affiliations:
Systems and Bioengineering Department, School of Engineering, Cairo University, Giza, Egypt
Venue:
EURASIP Journal on Applied Signal Processing
Year:
2005

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Abstract

Stochastic calculus methods are used to estimate the instantaneous frequency of a signal. The frequency is modeled as a polynomial in time. It is assumed that the phase has a Brownian-motion component. Using stochastic calculus, one is able to develop a stochastic differential equation that relates the observations to instantaneous frequency. Pseudo-maximum likelihood estimates are obtained through Girsanov theory and the Radon-Nikodym derivative. Bootstrapping is used to find the bias and the confidence interval of the estimates of the instantaneous frequency. An approximate expression for the Cramér-Rao lower bound is derived. An example is given, and a comparison to existing methods is provided.