A speech processing system is provided which is operable to receive sets of signal values representative of a speech signal generated by a speech source as distorted by a transmission channel between the speech source and the speech processing system. The system stores data defining a predetermined function derived from a signal model which models both the speech source and the channel and defining a probability density function which gives, for a given set of model parameters, the probability that the signal model has those model parameters given that the signal model is assumed to have generated the received set of signal values. The system applies a current set of received signal values to the stored probability density function and then draws samples from it using a Gibbs sampler. The system then analyses the samples to determine a set of parameter values representative of the speech signal before it was distorted by the channel.