Eigenvalue decomposition of a parahermitian matrix : extraction of analytic eigenvalues
Weiss, Stephan and Proudler, Ian K. and Coutts, Fraser K. (2021) Eigenvalue decomposition of a parahermitian matrix : extraction of analytic eigenvalues. IEEE Transactions on Signal Processing, 69. pp. 722-737. ISSN 1053-587X (https://doi.org/10.1109/TSP.2021.3049962)
Preview |
Text.
Filename: Weiss_etal_IEEE_TOPS_2021_Eigenvalue_decomposition_of_a_parahermitian_matrix.pdf
Accepted Author Manuscript Download (1MB)| Preview |
Abstract
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.
ORCID iDs
Weiss, Stephan ORCID: https://orcid.org/0000-0002-3486-7206, Proudler, Ian K. and Coutts, Fraser K.;-
-
Item type: Article ID code: 75128 Dates: DateEvent28 February 2021Published8 January 2021Published Online3 January 2021AcceptedNotes: © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Subjects: Technology > Electrical engineering. Electronics Nuclear engineering Department: Faculty of Engineering > Electronic and Electrical Engineering
Technology and Innovation Centre > Sensors and Asset ManagementDepositing user: Pure Administrator Date deposited: 21 Jan 2021 14:57 Last modified: 11 Dec 2024 21:40 URI: https://strathprints.strath.ac.uk/id/eprint/75128