Enforcing eigenvector smoothness for a compact DFT-based polynomial eigenvalue decomposition
Coutts, Fraser Kenneth and Thompson, Keith and Pestana, Jennifer and Proudler, Ian and Weiss, Stephan (2018) Enforcing eigenvector smoothness for a compact DFT-based polynomial eigenvalue decomposition. In: 10th IEEE Workshop on Sensor Array and Multichannel Signal Processing, 2018-07-08 - 2018-07-11.
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Abstract
A variety of algorithms have been developed to compute an approximate polynomial matrix eigenvalue decomposition (PEVD). As an extension of the ordinary EVD to polynomial matrices, the PEVD will generate paraunitary matrices that diagonalise a parahermitian matrix. While iterative PEVD algorithms that compute a decomposition in the time domain have received a great deal of focus and algorithmic improvements in recent years, there has been less research in the field of frequency-based PEVD algorithms. Such algorithms have shown promise for the decomposition of problems of finite order, but the state-of-the-art requires a priori knowledge of the length of the polynomial matrices required in the decomposition. This paper presents a novel frequency-based PEVD algorithm which can compute an accurate decomposition without requiring this information. Also presented is a new metric for measuring a function's smoothness on the unit circle, which is utilised within the algorithm to maximise eigenvector smoothness for a compact decomposition, such that the polynomial eigenvectors have low order. We demonstrate through the use of simulations that the algorithm can achieve superior levels of decomposition accuracy to a state-of-the-art frequency-based method.
ORCID iDs
Coutts, Fraser Kenneth ORCID: https://orcid.org/0000-0003-2299-2648, Thompson, Keith ORCID: https://orcid.org/0000-0003-0727-7347, Pestana, Jennifer ORCID: https://orcid.org/0000-0003-1527-3178, Proudler, Ian and Weiss, Stephan ORCID: https://orcid.org/0000-0002-3486-7206;-
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Item type: Conference or Workshop Item(Paper) ID code: 64015 Dates: DateEvent8 July 2018Published30 April 2018AcceptedSubjects: Technology > Electrical engineering. Electronics Nuclear engineering Department: Faculty of Engineering > Electronic and Electrical Engineering
Technology and Innovation Centre > Sensors and Asset Management
Faculty of Science > Mathematics and StatisticsDepositing user: Pure Administrator Date deposited: 11 May 2018 14:08 Last modified: 03 Oct 2024 00:47 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/64015