Eigenvalue decomposition of a parahermitian matrix : extraction of analytic eigenvalues

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Weiss, Stephan and Proudler, Ian K. and Coutts, Fraser K. (2021) Eigenvalue decomposition of a parahermitian matrix : extraction of analytic eigenvalues. IEEE Transactions on Signal Processing, 69. pp. 722-737. ISSN 1053-587X (https://doi.org/10.1109/TSP.2021.3049962)

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Abstract

An analytic parahermitian matrix admits an eigenvalue decomposition (EVD) with analytic eigenvalues and eigenvectors except in the case of multiplexed data. In this paper, we propose an iterative algorithm for the estimation of the analytic eigenvalues. Since these are generally transcendental, we find a polynomial approximation with a defined error. Our approach operates in the discrete Fourier transform (DFT) domain and for every DFT length generates a maximally smooth association through EVDs evaluated in DFT bins; an outer loop iteratively grows the DFT order and is shown, in general, to converge to the analytic eigenvalues. In simulations, we compare our results to existing approaches.

ORCID iDs

Weiss, Stephan ORCID logoORCID: https://orcid.org/0000-0002-3486-7206, Proudler, Ian K. and Coutts, Fraser K.;
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