Linear Prediction Models

Abstract

Linear prediction modelling is used in a diverse area of applications such as data forecasting, speech recognition, low bit rate coding, model-based spectral analysis, interpolation, signal restoration etc. In statistical literature, linear prediction models are referred to as autoregressive (AR) processes. In this chapter we introduce the theory of linear prediction, and consider efficient methods for computation of the predictor coefficients. We study the forward, the backward and the lattice predictors, and consider various methods of formulation of the least squared error predictor coefficients. For the modelling of signals with a quasi-periodic structure, such as voiced speech, an extended linear predictor, that simultaneously utilises both the short and the long term correlation structures, is introduced. Finally the application of linear prediction in enhancement of noisy speech is considered. Further applications of linear prediction models, in this book, are in Chapter 11 on the interpolation of a sequence of lost samples, and in Chapters 12 and 13 on the detection and removal of impulsive noise and transient noise pulses.