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 ![]() | Item type: | Conference or Workshop Item(Paper) |
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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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