Linear Prediction in Matlab and Octave

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Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Spectral Envelope Examples

Spectral Envelope by Linear Prediction

Spectral Modeling Synthesis

Minimum-phase polynomials have all their zeros inside the unit circle of the complex plane. — Click for https://ccrma.stanford.edu/~jos/filters/Minimum_Phase_Polynomials.html

A filter is said to be stable if its impulse response decays to zero as time goes to infinity — Click for https://ccrma.stanford.edu/~jos/filters/Stability_Revisited.html

Click for http://octave.sourceforge.net/

Linear Prediction is an important signal modeling tool which captures correlation information in the form of prediction coefficients. In digital audio signal processing, linear prediction computes a superior spectral envelope that emphasizes spectral peaks. — Click for http://en.wikipedia.org/wiki/Linear_prediction

Click for http://www.mathworks.com/help/signal/index.html

A signal is typically a real-valued function of time. A discrete-time signal is typically a real-valued function of discrete time, and is therefore a time-ordered sequence of real numbers. — Click for http://ccrma.stanford.edu/~jos/filters/Definition_Signal.html

Matlab is a high-level scripting language for scientific computing — Click for https://ccrma.stanford.edu/~jos/matlab/

Click for https://ccrma.stanford.edu/~jos/mdft/Autocorrelation.html

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JOS Home Page

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Index of terms in JOS Website

Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Spectral Envelope Examples

Spectral Envelope by Linear Prediction

Spectral Modeling Synthesis

Linear Prediction in Matlab and Octave

In the above example, we implemented essentially the covariance method of LP directly (the autocorrelation estimate was unbiased). The code should run in either Octave or Matlab with the Signal Processing Toolbox.

The Matlab Signal Processing Toolbox has the function lpc available. (LPC stands for ``Linear Predictive Coding.'')

The Octave-Forge lpc function (version 20071212) is a wrapper for the lattice function which implements Burg's method by default. Burg's method has the advantage of guaranteeing stability ( is minimum phase) while yielding accuracy comparable to the covariance method. By uncommenting lines in lpc.m, one can instead use the ``geometric lattice'' or classic autocorrelation method (called ``Yule-Walker'' in lpc.m). For details, ``type lpc''.

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Linear Prediction in Matlab and Octave

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University