Stability of linear predictors and numerical range of a linear operator

Authors:
P. Delsarte;Y. Genin;Y. Kamp
Affiliations:
Philips Research Laboratory, Brussels, Belgium;Philips Research Laboratory, Brussels, Belgium;Philips Research Laboratory, Brussels, Belgium
Venue:
IEEE Transactions on Information Theory
Year:
1987

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Abstract

The zeros of a predictor polynomial are shown to belong to the numerical range of a linear operator associated with the particular prediction problem considered. Application of this result to the autocorrelation and postwindowed cases shows that the predictor polynomials enjoy a well-defined stability margin which depends in particular on the length of the data sequence. The generalization of these results to the multichannel case is also discussed.