Superfast Approximative Implementation of the IAA Spectral Estimate

Authors:
G. O. Glentis;A. Jakobsson
Affiliations:
Department of Science and Technology of Telecommunications, University of Peloponnese, Tripolis, Greece;Dept. of Mathematical Statistics, Lund University, Lund, Sweden
Venue:
IEEE Transactions on Signal Processing
Year:
2012

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Abstract

In this correspondence, we develop superfast approximative one-dimensional algorithms for the computationally efficient implementation of the recent iterative adaptive approach (IAA) spectral estimate. The proposed methods are based on rewriting the IAA algorithm with suitable Gohberg–Semencul representations, solving the resulting linear systems of equations using the preconditioned conjugate gradient method, where a novel preconditioning is applied using an incomplete factorization of the Toeplitz matrix. Numerical simulations illustrate the efficiency of both the proposed preconditioning as well as the overall algorithm, offering a computational reduction of up to two orders of magnitude as compared to our recently proposed efficient and exact IAA implementation.