Abstract
The Wiener-Levinson method and algorithm, formulated here in terms of Szegö polynomials ρ n (ψ N,I ;z) orthogonal on the unit circle, is used to find unknown frequencies ω j from anN-sample of a discrete time signal consisting of the superposition of sinusoidal waves with frequencies ω1,...,ω1. In a recent paper the authors (and W.J. Thron) have shown that zerosz(j, n, N, I) of ρ n (ψ N,I ;z) converge asN→∞ to the critical points\(e^{i\omega _j } \),j=1, 2,...,I, providedn≥n 0 (I)=2I+L, whereL is 0 or 1. The present paper gives results on the convergence of zerosz(j, n, N, I) to some of the\(e^{i\omega _j } \) for the case in whichn≤n 0 (I), wheren is the degree of ρ n (ψ N,I ;z).
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Research supported in part by the United States Educational Foundation in Norway (Fulbright Grant), the Norwegian Research Council (NAVF) and the US National Science Foundation under Grant No. DMS-9103141.
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Jones, W.B., Njåstad, O. & Waadeland, H. Asymptotics for Szegö polynomial zeros. Numer Algor 3, 255–264 (1992). https://doi.org/10.1007/BF02141934
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DOI: https://doi.org/10.1007/BF02141934