A New Probabilistic Spectral Pitch Estimator: Exact and MCMC-approximate Strategies

Abstract

We propose a robust probabilistic pitch (f ₀) estimator in the presence of interference and low SNR conditions, without the computational requirements of optimal time-domain methods. Our analysis is driven by sinusoidal peaks extracted by a windowed STFT. Given f ₀ and a reference amplitude (A ₀), peak frequency/amplitude observations are modeled probabilistically in order to be robust to undetected harmonics, spurious peaks, skewed peak estimates, and inherent deviations from ideal or other assumed harmonic structure. Parameters f ₀ and A ₀ are estimated by maximizing the observations’ likelihood (here A ₀ is treated as a nuisance parameter). Some previous spectral pitch estimation methods, most notably the work of Goldstein [3], introduce a probabilistic framework with a corresponding maximum likelihood approach. However, our method significantly extends the latter in order to guarantee robustness under adverse conditions, facilitating possible extensions to the polyphonic context. For instance, our addressing of spurious as well as undetected peaks averts a sudden breakdown under low-SNR conditions. Furthermore, our assimilation of peak amplitudes facilitates the incorporation of timbral knowledge. Our method utilizes a hidden, discrete-valued descriptor variable identifying spurious/undetected peaks. The likelihood evaluation, requiring a computationally unwieldy summation over all descriptor states, is successfully approximated by a MCMC traversal chiefly amongst high-probability states. The MCMC traversal obtains virtually identical evaluations for the entire likelihood surface at a fraction of the computational cost.