First Grant research note: Audio time-frequency analysis as probabilistic inference

This research note proposes a new view of audio time-frequency analysis as a probilistic inference problem. That is, given an incoming signal, the goal is to infer the underlying the time-frequency coefficients using Bayes’ rule. The note begins by building a bridge between this inferential view of audio time-frequency analysis and traditional approaches, providing examples of inference problems that have optimal solutions corresponding to the short time-Fourier transform, spectrogram, filter bank, and wavelet representations. The same framework unifies a number of existing probabilistic models for audio time-series, which simplifies the literature substantially. The new theoretical perspective addresses three practical limitations of classical time-frequency analysis since well developed tools of probabilistic inference can be applied. First parameter learning methods can be used to adapt the properties of the time-frequency representation to the possibly changing statistics of the signal. Second, probabilistic methods naturally handle uncertainty, meaning the new time-frequency representations can be extended to noisy and missing data settings. Finally, and perhaps most importantly, the modularity of probabilistic methods enables them to be extended and improved.