An approximate Bayesian fundamental frequency estimator

Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency and the model order is based on a probability model which corresponds to a minimum of prior information. From this probability model, we give the exact posterior distributions on the fundamental frequency and the model order, and we also present analytical approximations of these distributions which lower the computational load of the algorithm. By use of simulations on both a synthetic signal and a speech signal, the algorithm is demonstrated to be more accurate than a state-of-the-art maximum likelihood-based method.