Model-Based STFT Phase Recovery for Audio Source Separation

Abstract

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.

Reducing Interference with Phase Recovery in DNN-based Monaural Singing Voice Separation

“…It has been used in many audio applications, including time stretching [23], speech enhancement [22] and source separation [7,11,24].…”

“…Another phase retrieval algorithm has been introduced in [7]. This approach aims at minimizing the mixing error:…”

“…Those approaches result in assigning the mixture's phase to the STFT voice estimate. However, even if the latter leads to quite satisfactory results in practice [2,3], it has been pointed out that when sources overlap in the TF domain, the assignment of the mixture's phase to the STFT voice estimate is responsible for residual interference and artifacts in the separated signals [7]. In the recent years, some efforts have been made to improve phase recovery in audio source separation.…”

“…In the recent years, some efforts have been made to improve phase recovery in audio source separation. Phase recovery algorithms exploit phase constraints that originate from consistency [8], a property of the STFT that arises from its redundant signal representation, or from a signal model that approximates time-domain signals as a sum of sinusoids [7]. The above mentioned phase constraints have been applied to a source separation task [9,7] and combined with magnitude estimation techniques in order to design full and phase-aware separation systems [10,11].…”

“…Phase recovery algorithms exploit phase constraints that originate from consistency [8], a property of the STFT that arises from its redundant signal representation, or from a signal model that approximates time-domain signals as a sum of sinusoids [7]. The above mentioned phase constraints have been applied to a source separation task [9,7] and combined with magnitude estimation techniques in order to design full and phase-aware separation systems [10,11]. However, these systems are based on variants of NMF methods, which provides fairly good separation results in scenarios where the sources are well represented with stationary spectral atoms (over time) and uniform temporal activations (over frequencies).…”