Enhancing the Tracking of Partials for the Sinusoidal Modeling of Polyphonic Sounds

This paper addresses the problem of tracking partials, i.e., determining the evolution over time of the parameters of a given number of sinusoids with respect to the analyzed audio stream. We first show that the minimal frequency difference heuristic generally used to identify continuities between local maxima of successive short-time spectra can be successfully generalized using the linear prediction formalism to handle modulated sounds such as musical tones with vibrato. The spectral properties of the evolutions in time of the parameters of the partials are next studied to ensure that the parameters of the partials effectively satisfy the slow time-varying constraint of the sinusoidal model. These two improvements are combined in a new algorithm designed for the sinusoidal modeling of polyphonic sounds. The comparative tests show that onsets/offsets of sinusoids as well as closely spaced sinusoids are better identified and stochastic components are better avoided.