Compression is achieved by building a predictive model of the waveform (a good introduction for speech is Jayant and Noll ). An established model for a wide variety of waveforms is that of an autoregressive model, also known as linear predictive coding (LPC). Here the predicted waveform is a linear combination of past samples:
The coded signal, , is the difference between the estimate of the linear predictor, and the speech signal, .
However, many waveforms of interest are not stationary, that is the best values for the coefficients of the predictor, , vary from one section of the waveform to another. It is often reasonable to assume that the signal is pseudo-stationary, i.e. there exists a time-span over which reasonable values for the linear predictor can be found. Thus the three main stages in the coding process are blocking, predictive modelling, and residual coding.