Real-time adaptive linear prediction using the least mean square gradient algorithm

Adaptive linear prediction (ALP) recently has received a great deal of attention for spectral analysis, system modeling, and speech encoding. The conventional approach used to implement ALP involves the computation of a sample covariance matrix for a block of data and solution of an associated set of simultaneous equations to obtain the predictor coefficients. This paper describes an alternate approach that uses the least mean square (LMS) gradient, stochastic-approximation algorithm, commonly used in many other adaptive systems. A complete 8-coefficient hardward system based on this approach has been designed and constructed and is described in this paper. The system consists of an analyzer that computes the eight ALP coefficients in real time and a reconstructor that forms an all-pole model filter using the computed coefficients. Several examples are presented to illustrate the concepts introduced. Each example includes an analytical discussion followed by experimental verification. Applications of ALP for spectral analysis, instantaneous frequency measurement, and speech encoding are discussed and experimental results obtained with the real-time hardware are presented.