Multi-pitch Estimation using Semidefinite Programming

Multi-pitch estimation concerns the problem of estimating the fundamental frequencies (pitches) and amplitudes/phases of multiple superimposed harmonic signals with application in music, speech, vibration analysis etc. In this paper we formulate a complex-valued multi-pitch estimator via a semidefinite programming representation of an atomic decomposition over a continuous dictionary of complex exponentials and extend this to real-valued data via a real semidefinite pro-ram with the same dimensions (i.e. half the size). We further impose a continuous frequency constraint naturally occurring from assuming a Nyquist sampled signal by adding an additional semidefinite constraint. We show that the proposed estimator has superior performance compared to state-
of-the-art methods for separating two closely spaced fundamentals and approximately achieves the asymptotic Cramér-Rao lower bound.