Bayesian formulation of subband autoregressive modelling with boundary continuity constraints

The all-pole model is often used to approximate rational transfer functions parsimoniously. In many applications, such as single channel blind deconvolution, an estimate of the channel is required. However, in general, attempting to model the entire channel spectrum by a single all-pole model leads to a large computational load. Hence, it is better to model a particular frequency band of the spectrum by an all-pole model, reducing a single high-dimensional optimisation to a number of low-dimensional ones. If each subband is completely decoupled from the others, and does not enforce any continuity, there are discontinuities in the spectrum at the subband boundaries. Continuity is ensured by constraining the subband parameters such that the end points at one subband boundary are matched to the spectrum in the adjacent subbands. This is formulated in the Bayesian probabilistic framework.