Bertrand David

Paul Magron, Roland Badeau, Bertrand David

For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the corresponding complex-valued STFT. Most authors in this field choose a Wiener-like filtering approach which boils down to using the phase of the original mixture. In this paper, a different standpoint is adopted. Many music events are partially composed of slowly varying sinusoids and the STFT phase increment over time of those frequency components takes a specific form. This allows phase recovery by an unwrapping technique once a short-term frequency estimate has been obtained. Herein, a novel iterative source separation procedure is proposed which builds upon these results. It consists in minimizing the mixing error by means of the auxiliary function method. This procedure is initialized by exploiting the unwrapping technique in order to generate estimates that benefit from a temporal continuity property. Experiments conducted on realistic music pieces show that, given accurate magnitude estimates, this procedure outperforms the state-of-the-art consistent Wiener filter.

Paul Magron, Roland Badeau, Bertrand David

Phase recovery of modified spectrograms is a major issue in audio signal processing applications, such as source separation. This paper introduces a novel technique for estimating the phases of components in complex mixtures within onset frames in the Time-Frequency (TF) domain. We propose to exploit the phase repetitions from one onset frame to another. We introduce a reference phase which characterizes a component independently of its activation times. The onset phases of a component are then modeled as the sum of this reference and an offset which is linearly dependent on the frequency. We derive a complex mixture model within onset frames and we provide two algorithms for the estimation of the model phase parameters. The model is estimated on experimental data and this technique is integrated into an audio source separation framework. The results demonstrate that this model is a promising tool for exploiting phase repetitions, and point out its potential for separating overlapping components in complex mixtures.

Paul Magron, Roland Badeau, Bertrand David

This paper introduces a novel technique for reconstructing the phase of modified spectrograms of audio signals. From the analysis of mixtures of sinusoids we obtain relationships between phases of successive time frames in the Time-Frequency (TF) domain. To obtain similar relationships over frequencies, in particular within onset frames, we study an impulse model. Instantaneous frequencies and attack times are estimated locally to encompass the class of non-stationary signals such as vibratos. These techniques ensure both the vertical coherence of partials (over frequencies) and the horizontal coherence (over time). The method is tested on a variety of data and demonstrates better performance than traditional consistency-based approaches. We also introduce an audio restoration framework and observe that our technique outperforms traditional methods.