  In audio signal processing, probabilistic time-frequency models have many
benefits over their non-probabilistic counterparts. They adapt to the incoming
signal, quantify uncertainty, and measure correlation between the signal's
amplitude and phase information, making time domain resynthesis
straightforward. However, these models are still not widely used since they
come at a high computational cost, and because they are formulated in such a
way that it can be difficult to interpret all the modelling assumptions. By
showing their equivalence to Spectral Mixture Gaussian processes, we illuminate
the underlying model assumptions and provide a general framework for
constructing more complex models that better approximate real-world signals.
Our interpretation makes it intuitive to inspect, compare, and alter the models
since all prior knowledge is encoded in the Gaussian process kernel functions.
We utilise a state space representation to perform efficient inference via
Kalman smoothing, and we demonstrate how our interpretation allows for
efficient parameter learning in the frequency domain.
