Multi-pitch estimation of inharmonic signals

This work presents a relaxation-based multi-pitch estimation technique for harmonic signals suffering from inharmonicity. Different from most earlier works, the proposed method does not require a priori knowledge of the number of sources present, nor of their respective number of harmonics, or the inharmonicity structure of the expected deviations. Using a recent group-sparse multi-pitch estimation method to form initial coarse pitch estimates, the number of sources and their harmonics are estimated using a BIC-based formulation, whereafter an iterative, relaxation-based, technique is formed to separately estimate the inharmonicity of each source using a recently proposed robust single-pitch estimation technique. The proposed algorithm is evaluated and compared to other existing methods using both simulated and real audio signals, clearly illustrating the improved performance.