Unifying Probabilistic Models for Time-Frequency Analysis
This work addresses interpretability and efficiency challenges for researchers and practitioners in audio signal processing, though it is incremental as it builds on existing probabilistic models.
The paper tackled the high computational cost and interpretability issues of probabilistic time-frequency models in audio signal processing by showing their equivalence to Spectral Mixture Gaussian processes, resulting in a framework that enables efficient inference via Kalman smoothing and parameter learning in the frequency domain.
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.