Robust Fundamental Frequency Estimation in the Presence of Inharmonicities

We develop a general robust fundamental frequency estimator that allows for non-parametric inharmonicities in the observed signal. To this end, we incorporate the recently developed multi-dimensional covariance fitting approach by allowing the Fourier vector corresponding to each perturbed harmonic to lie within a small uncertainty hypersphere centered around its strictly harmonic counterpart. Within these hyperspheres, we find the best perturbed vectors fitting the covariance of the observed data. The proposed approach provides the estimate of the fundamental frequency in two steps, and, unlike other recentmethods, involves only a single 1-D search over a range of candidate fundamental frequencies. The proposed algorithm is numerically shown to outperform the current competitors under a variety of practical conditions, including various degrees of inharmonicity and different levels of noise.