%0 Journal Article
%T Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping
%A A. Abutaleb
%J EURASIP Journal on Advances in Signal Processing
%D 2005
%I Springer
%R 10.1155/asp.2005.1886
%X 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 Cram    r-Rao lower bound is derived. An example is given, and a comparison to existing methods is provided.
%K bootstrapping
%K Ito calculus
%K instantaneous frequency
%K time-varying frequency
%K Girsanov theory.
%U http://dx.doi.org/10.1155/ASP.2005.1886