Extraction of analytic eigenvectors from a parahermitian matrix

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

Research output: Contribution to conferencePaper

Abstract

The space-time covariance matrix derived from broadband multichannel data admits — unless the data emerges from a multiplexing operation — a parahermitian matrix eigenvalue decomposition with analytic eigenvalues and analytic eigenvectors. The extraction of analytic eigenvalues has been solved previously in the discrete Fourier transform (DFT) domain; this paper addresses the approximation of analytic eigenvectors in the DFT domain. This is a two-stage process — in the first instance, we identify eigenspaces in which analytic eigenvectors can reside. This stage resolves ambiguities at frequencies where eigenvalues have algebraic mulitplicities greater than one. In a second stage, the phase ambiguity of eigenvectors is addressed by determining a maximally smooth phase response. Finally, a metric for the
approximation error is derived, which allows us to increase the DFT length and iterate the two stages until a desired accuracy is reached.
Original languageEnglish
Number of pages5
Publication statusAccepted/In press - 20 Jul 2020
EventInternational Conference on Sensor Signal Processing for Defence - Edinburgh, United Kingdom
Duration: 15 Sep 202016 Sep 2020
https://sspd.eng.ed.ac.uk/

Conference

ConferenceInternational Conference on Sensor Signal Processing for Defence
Abbreviated titleSSPD
CountryUnited Kingdom
CityEdinburgh
Period15/09/2016/09/20
Internet address

Keywords

  • eigenvectors
  • parahermitian matrices
  • space-time covariance matrix

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    Weiss, S., Proudler, I. K., Coutts, F. K., & Deeks, J. (Accepted/In press). Extraction of analytic eigenvectors from a parahermitian matrix. Paper presented at International Conference on Sensor Signal Processing for Defence, Edinburgh, United Kingdom.