Exact ARMA lattice predictors from autocorrelation functions

The paper derives an optimal linear L/sup 2/-predictor of ARMA-type in the lattice form of arbitrarily fixed dimensions for a process whose autocorrelation function is known. The algorithm preserves exact optimality at each step, as opposed to asymptotic convergence of more usual algorithms, at the...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 42; no. 4; pp. 877 - 886
Main Authors: Monin, A., Salut, G.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.1994
Institute of Electrical and Electronics Engineers
Subjects:
Applied sciences
Autocorrelation
Automatic
Convergence
Detection, estimation, filtering, equalization, prediction
Engineering Sciences
Exact sciences and technology
Feedback
Information, signal and communications theory
Lattices
Low pass filters
Random variables
Signal and communications theory
Signal processing algorithms
Signal, noise
Stochastic processes
Telecommunications and information theory
Vectors
Autocorrelation function
Autoregressive moving average
ARMA model
Linear prediction
Tchebychev filter
Predictor
reduced filters
Linear filtering
linear predictor
lattice form
ISSN:1053-587X
Online Access:Get full text
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Summary:The paper derives an optimal linear L/sup 2/-predictor of ARMA-type in the lattice form of arbitrarily fixed dimensions for a process whose autocorrelation function is known. The algorithm preserves exact optimality at each step, as opposed to asymptotic convergence of more usual algorithms, at the expense of hereditary computation. Only the discrete-time case is examined. It is shown how the unnormalized (respectively normalized) lattice form may be reduced to only 4n-2 parameters (respectively 2n+1) for a nth-order projection on the past. The normalization algorithm for the forward and backward residuals uses only scalar square root computations. Some examples that show the accuracy of this technique compared with those using the classical ARMA form for the predictor, are given.< >
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ISSN:1053-587X
DOI:10.1109/78.285651