Multidimensional optimisation of harmonic signals

Harmonic models are a common class of sinusoidal models which are of great interest in speech and musical analysis. In this paper we present a method for estimating the parameters of an unknown number of musical notes, each with an unknown number of harmonics. We pose the estimation task in a Bayesian framework which allows for the specification of (possibly subjective) a priori knowledge of the model parameters. We use indicator variables to represent implicitly the model order and employ a Metropolis-Hastings algorithm to produce approximate maximum a posteriori parameter estimates. A novel choice of transition kernels is presented to explore the parameter space, exploiting the structure of the posterior distribution.