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Linear prediction: A tutorial review

Makhoul, J.·1975·Proceedings of the IEEE
DOI 10.1109/proc.1975.9792
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Abstract

This paper gives an exposition of linear prediction in the analysis of discrete signals. The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal. In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum. The major part of the paper is devoted to all-pole models. The model parameters are obtained by a least squares analysis in the time domain. Two methods result, depending on whether the signal is assumed to be stationary or nonstationary. The same results are then derived in the frequency domain. The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra. This also leads to a discussion of the advantages and disadvantages of the least squares error criterion. A spectral interpretation is given to the normalized minimum prediction error. Applications of the normalized error are given, including the determination of an "optimal" number of poles. The use of linear prediction in data compression is reviewed. For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients. Finally, a brief introduction to pole-zero modeling is given.

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Metadata

Authors
Makhoul, J.
Venue
Proceedings of the IEEE
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
1975
Volume
63
Issue
4
Pages
561-580
ISSN
0018-9219 (ISSN-L)
DOI
10.1109/proc.1975.9792
OpenAlex
W1966264494
Cited by
4,023
References
5
FWCI
50.59
Type
journal article
Language
en
Open access
closed
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)

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