27-07-2012, 11:44 AM
linear Prediction: A Tutorial Review
Abstract
This paper gives an exposition of linear prediction in the
tion of its past values d 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 modeliug the signal spec- by a polezero
spectrum. The major part of the paper is devoted to all-pde
models. The model parameters are obtained by a least squares nnnlysis
in the time domain Two methods result, depending on whether the
signal is wsumed to be stationay or nonstationary. The same results
are then derived in the frequency domain. The resulting spectral matching
formulation allows for the modeling of sehted poltiom of a spectnun, for arbitrary spectral shaping in the frequency domain, and
for the modeling of continuous as well as discrete spectra. Thii also
lepds to a dslssion of the advrntnges and disodv~ntrgeso f the least
quues mor 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.
INTRODUCTION
A. Overview T HE MATHEMATICAL analysis of the behavior of general
dynamic systems (be they engineering, social, or
economic) has been an area of concern since the beginning
of this century. The problem has been pursued with
accelerated vigor since the advent of electronic digital computers
over two decades ago. The analysis of the outputs of
dynamic systems was for the most part the concern of “time
series analysis,” which was developed mainly within the fields
of statistics, econometrics, and communications. Most of the
work on time series analysis was actually done by statisticians.
More recently, advances in the analysis of dynamic systems
have been made in the field of control theory based on statespace
concepts and time domain analysis.