Extraction of analytic eigenvectors from a parahermitian matrix

Weiss, Stephan and Proudler, Ian K. and Coutts, Fraser K. and Deeks, Julian (2020) Extraction of analytic eigenvectors from a parahermitian matrix. In: International Conference on Sensor Signal Processing for Defence, 2020-09-15 - 2020-09-16.

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    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.

    Creators(s): Weiss, Stephan ORCID logoORCID: https://orcid.org/0000-0002-3486-7206, Proudler, Ian K., Coutts, Fraser K. and Deeks, Julian;
    Item type:Conference or Workshop Item(Paper)
    ID code:73296
    Keywords:eigenvectors, parahermitian matrices, space-time covariance matrix, Electrical engineering. Electronics Nuclear engineering, Electrical and Electronic Engineering
    Subjects:Technology > Electrical engineering. Electronics Nuclear engineering
    Department:Faculty of Engineering > Electronic and Electrical Engineering
    Technology and Innovation Centre > Sensors and Asset Management
    Depositing user: Pure Administrator
    Date deposited:22 Jul 2020 14:01
    Last modified:20 Jan 2021 15:09
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/73296
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