Linear prediction

Another well known method for converting the least-damped modes into parametric form is Linear Predictive Coding (LP) followed by polynomial factorization to obtain resonator poles. LP is particularly good at fitting spectral peaks due to the nature of the error criterion it minimizes [437]. The poles closest to the unit circle in the plane can be chosen for the ``ringy'' part of the resonator. It is well known that when using techniques like LP to model spectral peaks for extraction, orders substantially higher than twice the number of spectral peaks should be used. The extra degrees of freedom in the LP fit give more poles for modeling spectral detail other than the peaks, allowing the poles modeling the peaks to fit them with less distraction. On the other hand, if the order chosen is too high, sometimes more than two poles will home in on the same peak. In some cases, this may be appropriate since the body resonances are not necessary resolvable so as to separate the peaks, especially at high frequencies.

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written by 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.