Unified development of algorithms used for linear predictive coding of speech signals

The requirement for low data rate voice transmission has resulted in a large number of algorithms being proposed for speech digitization at data rates of 2·4–4 kilobits/sec. Many of the proposed algorithms are quite complicated and have their origin in disciplines generally considered to be outside of the realm of the speech researcher or communication system designer. Additionally, the algorithms have been developed and presented in highly varying notation using various theoretical approaches. The result is a confusing array of equations, algorithms, and numerical analysis procedure. It is the goal of this paper to alleviate this problem by providing a unified tutorial development of the various algorithms used and proposed for speech data compression.Classical least squares estimation theory is used as the focal point of the discussion since it forms the basis for several of the more familiar speech digitization algorithms. The remainder of the algorithms, whether they have their basis in stochastic estimation theory or statistical regression theory, are related back to the more familiar least squares approach. The speech digitization techniques discussed are the covariance method, the autocorrelation method, the PARCOR method, a priori analysis, the sequential least squares method, the Kalman filter approach, the stochastic approximation method, and the general linear regression model. An effort has been made to provide sufficient theoretical background to establish the algorithm relationships without stressing mathematical rigor.