Paul T. Troughton and Simon J. Godsill. MCMC methods for restoration of quantised time series. Proceedings of the IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, 2:447-451, 1999.

In digital systems, the amplitude of a time series is quantised with finite resolution. This is a nonlinear process which introduces distortion. We develop a Bayesian, model-based approach to reducing the quantisation distortion when moving a time series, such as an audio signal, to a higher resolution medium. The signal is modelled as a discrete-time, continuous-valued autoregressive (AR) process of unknown order. The model parameters and reconstructed signal are estimated using Markov chain Monte Carlo (MCMC) techniques. This requires samples to be drawn from a truncated multivariate Gaussian distribution, for which a Metropolis-Hastings approach is developed.