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.
['Philippe Delsarte', 'Y. Genin', 'Y. Kamp']
Stability of linear predictors and numerical range of a linear operator (Corresp.)