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Linear Prediction Methods

The two classic methods for linear prediction are called the autocorrelation method and the covariance method [162,157]. 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 6), and it has the desirable property that $ {\hat A}(z)$ is always minimum phase (i.e., $ 1/{\hat A}(z)$ 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 Bartlett-window bias in the sample autocorrelation.

The covariance method of LP is based on an unbiased autocorrelation estimate (see Eq.(6.4)). 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 [157].

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University