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Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping

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.

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Correspondence to A. Abutaleb.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abutaleb, A. Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping. EURASIP J. Adv. Signal Process. 2005, 172584 (2005). https://doi.org/10.1155/ASP.2005.1886

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Keywords and phrases:

  • bootstrapping
  • Ito calculus
  • instantaneous frequency
  • time-varying frequency
  • Girsanov theory