Eigenvalue decomposition of a parahermitian matrix: extraction of analytic eigenvalues

Stephan Weiss, Ian K. Proudler, Fraser K. Coutts

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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.
Original languageEnglish
Pages (from-to)722-737
Number of pages16
JournalIEEE Transactions on Signal Processing
Early online date8 Jan 2021
Publication statusE-pub ahead of print - 8 Jan 2021


  • eigenvalue
  • eigenfunctions
  • matrix decomposition
  • covariance matrices
  • approximation algorithms

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