Statistical inference for single- and multi-band Probabilistic Amplitude Demodulation

Amplitude demodulation is an ill-posed problem and so it is natural to treat it from a Bayesian viewpoint, inferring the most likely carrier and envelope under probabilistic constraints. One such treatment is Probabilistic Amplitude Demodulation (PAD), which, whilst computationally more intensive than traditional approaches, offers several advantages. Here we provide methods for estimating the uncertainty in the PAD-derived envelopes and carriers, and for learning free parameters like the time-scale of the envelope. We show how the probabilistic approach can naturally handle noisy and missing data. Finally, we indicate how to extend the model to signals which contain multiple modulators and carriers.