Probabilistic phase vocoder and its application to interpolation of missing values in audio signals

We formulate the phase vocoder - an audio synthesis method very closely related to inverse short time Fourier Transform synthesis - as a Gaussian state space model and demonstrate simulation results on interpolation of missing values. The audio signal is modelled as a superposition of quasi-sinusoidal signals generated by a linear dynamical system. The advantage of our “generative” perspective is that it allows a full Bayesian treatment of the problem; e.g. one can perform the analysis while arbitrary chunks of sample values are missing or model parameters are unknown. To perform audio restoration, we derive an expectation-maximisation (EM) algorithm that infers the expectations of missing samples and maximum a-posteriori model parameters. We demonstrate the validity of our approach on a set of challenging real audio examples and compare to existing methods.