Joint fundamental frequency and order estimation using optimal filtering

In this paper, the problem of jointly estimating the number of harmonics and the fundamental frequency of periodic signals is considered. We show how this problem can be solved using a number of methods that either are or can be interpreted as filtering methods in combination with a statistical model selection criterion. The methods in question are the classical comb filtering method, a maximum likelihood method, and some filtering methods based on optimal filtering that have recently been proposed, while the model selection criterion is derived herein from the maximum a posteriori principle. The asymptotic properties of the optimal filtering methods are analyzed and an order-recursive efficient implementation is derived. Finally, the estimators have been compared in computer simulations that show that the optimal filtering methods perform well under various conditions. It has previously been demonstrated that the optimal filtering methods perform extremely well with respect to fundamental frequency estimation under adverse conditions, and this fact, combined with the new results on model order estimation and efficient implementation, suggests that these methods form an appealing alternative to classical methods for analyzing multi-pitch signals.