Linear Prediction Methods

The two classic methods for linear prediction are called the autocorrelation method and the covariance method [153,148]. Both methods solve the linear normal equations (defined below) using different autocorrelation estimates.

In the autocorrelation method of linear prediction, the covariance matrix is constructed from the usual Bartlett-window-biased sample autocorrelation function (see Chapter 5), and it has the desirable property that is always minimum phase (i.e., is guaranteed to be stable). However, the autocorrelation method tends to overestimate formant bandwidths; in other words, the filter model is typically overdamped. This can be attributed to implicitly ``predicting zero'' outside of the signal frame, resulting in the Bartlet-window bias in the sample autocorrelation.

The covariance method of LP is based on an unbiased autocorrelation estimate (see Eq.(5.1)). As a result, it gives more accurate bandwidths, but it does not guarantee stability.

So-called covariance lattice methods and Burg's method were developed to maintain guaranteed stability while giving accuracy comparable to the covariance method of LP [148].

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.