Linear Prediction is Peak Sensitive

By Rayleigh's energy theorem, (as shown in §2.3.8). Therefore,

From this ``ratio error'' expression in the frequency domain, we can see that contributions to the error are smallest when . Therefore, LP tends to overestimate peaks. LP cannot make arbitrarily large because is constrained to be monic and minimum-phase. It can be shown that the log-magnitude frequency response of every minimum-phase monic polynomial is zero-mean [153]. Therefore, for each peak overestimation, there must be an equal-area ``valley underestimation'' (in a log-magnitude plot over the unit circle).

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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.