Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping | EURASIP Journal on Applied Signal Processing 2005 12 1886-1901 2005 Hindawi Publishing Corporation Instantaneous Frequency Estimation Using Stochastic Calculus and Bootstrapping A. Abutaleb Systems and Bioengineering Department School of Engineering Cairo University 12613 Giza Egypt Email ataleb@. eg Received 15 July 2004 Revised 6 March 2005 Recommended for Publication by Frank Ehlers 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 Cramer-Rao lower bound is derived. An example is given and a comparison to existing methods is provided. Keywords and phrases bootstrapping Ito calculus instantaneous frequency time-varying frequency Girsanov theory. 1. INTRODUCTION Over the past several years there has been a marked increase in the application of coherent signal and image processing. Coherent processing requires an accurate estimate of the phase Blackledge 1 . Examples where coherent processing is required include synthetic aperture radar SAR synthetic aperture sonar adaptive beam forming acoustic imaging projection and diffraction tomography adaptive optics magnetic resonance imaging MRI and inverse synthetic aperture radar ISAR see Goldstein et al. 2 Song et al. 3 Ghiglia and Pritt 4 . Phase estimation also has many applications in the areas of radar Wehner 5 and communications Li 6 and others. The instantaneous frequency IF is defined as the derivative of the phase. There are mainly two approaches for the estimation
