Linear Prediction is Peak Sensitive

By Rayleigh's energy theorem (Parseval's theorem):

From this ``ratio error'' expression in the frequency domain, we can see the following:

• Contributions to the error are smallest when .
• Therefore, LP tends to overestimate peaks.
• LP cannot set because the log of the amplitude response of every minimum-phase monic polynomial is zero-mean.

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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.