Formulations

Abstract

The first application of linear prediction to speech from a maximum likelihood formulation was in the work of Saito and Itakura in 1966. In 1967 and 1968, Atal and Schroeder [1967, 1968 b, 1968 c] published results on predictive coding of speech signals. Itakura and Saito also published a condensed English version of the maximum likelihood estimation procedure in 1968 and a detailed presentation in 1970. In 1970, Atal [1970 a] presented the first use of the term linear prediction for speech analysis. Since that time, the term has become universally accepted as referring to those methods of speech analysis that result in the solution of a predictor filter or inverse filter based upon solving a set of M linear simultaneous equations (as discussed in Chapter 1). In 1970, Markel [1971a] discussed the application of Prony’s method to speech analysis and noted the relationships to the linear prediction method developed by Atal and the maximum likelihood method developed by Itakura and Saito.