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.
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 shortterm 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.
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