Linear Prediction Spectral Envelope

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Linear prediction itself:

$\displaystyle y(n) = -a_1 y(n-1) - a_2 y(n-2) - \cdots - a_M y(n-M) + e(n)$

Signal is predicted from its past samples
is the prediction error or innovations sequence
Spectral Model:

$\begin{eqnarray*} Y(z) &=& \frac{E(z)}{A(z)} \\ &\approx& {\hat Y}(z) \;\isdef \; \frac{{\hat \sigma}_e}{{\hat A}(z)} \end{eqnarray*}$
Prediction error is spectrally flat
( approximates white noise or an impulse).

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.

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