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.

The paper proposes to improve further the tracking of partials in a polyphonic context. Spectral characteristics of the controlling parameters (amplitude and frequency) are taken into account to ensure that these parameters evolve slowly with time. The resulting algorithm tracks closely-spaced sinusoids better and is able to avoid most of the spectral data belonging to noise. As a consequence, the proposed algorithm extracts a more meaningful sinusoidal representation from polyphonic recordings.

In this article, we present an enhanced algorithm, of low complexity, for the tracking of partials in the context of sinusoidal modeling. By considering the past evolution of each partial in the time/frequency and time/amplitude planes to predict its future evolutions, this algorithm allows a better discrimination between sinusoidal and noisy components and an easier cancellation of sudden changes in the evolutions of the partials.

The design of filter banks for source coding purposes classically relies on the perfect reconstruction (PR) property. However, several studies have shown that taking the quantization noise into account in the design could yield a noticeable reduction of the mean square reconstruction error. The purpose of this study is to show that perceptual improvement can also be obtained in the particular audio coding context by relaxing the PR constraint. In this context, the mean square error is not relevant any more, and we define a new perceptual distortion criterion, making use of a simplified ear model, the MPE (mean perceptual error). Then, synthesis filters are optimized so as to minimize this MPE. Finally, this MMPE (minimum MPE) filter bank is included in an audio coding scheme. Compared to the corresponding PR filter bank-based scheme by the means of POM (perceptual objective measure), they show an improved audio quality.