Phase recovery by unwrapping: applications to music signal processing

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. Instantaneous frequencies are estimated locally to encompass the class of non-stationary signals such as vibratos. This technique ensures the horizontal coherence (over time) of the partials. 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 obtain results that compete with other state-of-the-art methods. Finally, we apply this phase recovery method to an audio source separation task where the spectrograms of the isolated components are known. We propose to use the phase unwrapping estimate to initialize a source separation iterative procedure. Experiments conducted on realistic music pieces demonstrate the effectiveness of such a method for various music signal processing tasks.