Processing of chirp and chirplet signals by MCMC methods.

摘要

Frequency-domain signal processing techniques have been used significantly. Although the Fourier expansion provides excellent representation of a broad class of signals, this is not so when the signals are not globally stationary. A typical example is the family of chirp signals.; Changing frequencies is the characteristic of chirp signals; in addition, the spectra of chirp signals are also time-varying. Recently time-frequency representations (TFRs) have been introduced to describe how the frequency content of a chirp signal evolves to develop the physical and mathematical ideas needed to understand what time-varying spectra are.; The objective of this work is to develop new methods for parameter estimation of chirp signals and chirplet signals, which are chirp signals with Gaussian-shape envelope. The applied methodology is Bayesian. In the Bayesian approach, knowledge about unknown quantities is represented in the form of probability distributions. Instead of obtaining point estimates of unknowns, the Bayesian approach estimates the posterior distributions of the unknowns, which requires performing multi-dimensional integrations. Sometimes, it is very difficult to carry out the integrations either analytically or numerically. This setback can be overcome by using Markov Chain Monte Carlo (MCMC) sampling technique.; We also address the estimation problem of unknown number of chirplets and their parameters. We apply the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method to solve this problem.; Our main contributions to the parameter estimation of chirp signals are as follows: finding the difficulties of estimation, investigating the relations among parameters and employing the MCMC techniques.; At the end of each chapter, we provide simulation results that illustrate our approach.