Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping


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.

DOI: 10.1155/ASP.2005.1886

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@article{Abutaleb2005InstantaneousFE, title={Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping}, author={Ahmed S. Abutaleb}, journal={EURASIP J. Adv. Sig. Proc.}, year={2005}, volume={2005}, pages={1886-1901} }