Bayesian analysis of generalized frequency-modulated signals

General frequency-modulated (GFM) signals can be used to characterize many vibrations in dynamic environments, with applications to engine monitoring and sonar. Most work into parameter estimation of such signals assumes knowledge of the number of carrier frequencies. In this paper, we make no such assumption and use Bayesian techniques to address jointly the problem of model selection and parameter estimation. Following the work of Andrieu and Doucet (see ibid., vol.47, p.2667-76, 1999), who addressed the problem for nonmodulated sinusoids, a posterior distribution for the parameters and model order is obtained. This distribution is too complicated for analytical extraction of moments and to sample from directly; therefore, we use a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to draw samples from the distribution. Some simulated examples are presented to illustrate the algorithm´s performance