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
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 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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