On modeling the STFT phase of audio signals with the von Mises distribution

In this paper, we study statistical models for the phase of the short-term Fourier transform (STFT) of audio signals. STFT phase globally appears as uniformly distributed, which has led researchers in this field to model it as a uniform random variable. However, some information about the phase can be obtained from a sinusoidal model, which reveals its local structure. Therefore, we propose to model the phase with a von Mises (VM) random variable, which enables us to favor the sinusoidal model-based phase value. We estimate the distribution parameters and we validate this model on real audio data. In particular, we observe that both models (uniform and VM) are relevant from a statistical perspective but they convey different information about the phase (global vs. local). We also apply this VM model to an audio source separation task, where it outperforms previous approaches.