Modification of a method using Szego polynomials in frequency analysis: the V-process

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:133

Article; Proceedings Paper

Petersen, V

关键词: frequency analysis;    Szego polynomial;    zeros;    Toeplitz determinant;   

DOI  :  10.1016/S0377-0427(00)00674-9

来源: Elsevier

【 摘 要 】

Recently, a method has been established for determining the n(0) unknown frequencies omega (j) in a trigonometric signal by using Szego polynomials, rho (n)(psi (N); z). Essential in the study is the asymptotic behavior of the zeros. If n greater than or equal ton(0) then n(0) of the zeros in the limit polynomial will tend to the frequency points e(+/-i omega).The remaining (n-n(0)) are bounded away from the unit circle. Several modifications of this method are developed. The modifications are of two main types: Modifying the observed signal values or modifying the moments. In the present paper we will replace the moment sequence {mu ((N))(m)/N} by a new sequence {(mu (m)(N)/N)Rm(2)}, where R is an element of (0, 1). In this situation we prove the surprising result that a multiple of the no zeros tend to the frequency points. We also prove the rate at which certain Toeplitz determinants tend to zero. (C) 2001 Elsevier Science B.V. All rights reserved.

【 授权许可】

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