8 Linear Prediction Models

inear prediction modelling is used in a diverse area of applications, such as data forecasting, speech coding, video coding, speech recognition, model-based spectral analysis, model-based interpolation, signal restoration, and impulse/step event detection. In the statistical literature, linear prediction models are often referred to as autoregressive (AR) processes. In this chapter, we introduce the theory of linear prediction modelling and consider efficient methods for the computation of predictor coefficients. We study the forward, backward and lattice predictors, and consider various methods for the formulation and calculation of predictor coefficients, including the least square error and maximum a posteriori methods. For the modelling of signals with a quasiperiodic structure, such as voiced speech, an extended linear predictor that simultaneously utilizes the short and long-term correlation structures is introduced. We study sub-band linear predictors that are particularly useful for sub-band processing of noisy signals. 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. L z – 1 z – 1 z– 1 . . . u(m)