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
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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Computation of Linear Prediction Coefficients
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Linear Prediction is Peak Sensitive