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Abstract
Parahermitian matrices in almost all cases admit an eigenvalue decomposition (EVD) with analytic eigenvalues. This decomposition is key in order to extend the utility of the EVD from narrowband multichannel signal processing problems to the broadband case, where the EVD factors are frequency dependent. In the frequency domain, the ground truth analytic eigenvalues may intersect, in this paper we discuss why with estimated spacetime covariance matrices such algebraic multiplicities are lost, resulting with probability one in analytic, spectrally majorised eigenvalues that no longer intersect. We characterise this phenomenon and some of its profound consequences for broadband multichannel array signal processing.
Original language  English 

Pages  15 
Number of pages  5 
Publication status  Published  3 Nov 2022 
Event  56th Asilomar Conference on Signals, Systems, and Computers  Pacific Grove, CA, United States Duration: 30 Nov 2021 → 3 Nov 2022 https://www.asilomarsscconf.org/ 
Conference
Conference  56th Asilomar Conference on Signals, Systems, and Computers 

Abbreviated title  Asilomar'22 
Country/Territory  United States 
Period  30/11/21 → 3/11/22 
Internet address 
Keywords
 spacetime covariance
 polynomial eigenvalue decomposition
 analytic eigenvalue decomposition
 estimation
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Dive into the research topics of 'Spacetime covariance matrix estimation: loss of algebraic multiplicities of Eigenvalues'. Together they form a unique fingerprint.Projects
 1 Active

Signal Processing in the Information Age (UDRC III)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 31/03/24
Project: Research

Eigenvalue decomposition of a parahermitian matrix: extraction of analytic eigenvalues
Weiss, S., Proudler, I. K. & Coutts, F. K., 28 Feb 2021, In: IEEE Transactions on Signal Processing. 69, p. 722737 16 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile10 Citations (Scopus)43 Downloads (Pure) 
Sample spacetime covariance matrix estimation
Delaosa, C., Pestana, J., Goddard, N. J., Somasundaram, S. & Weiss, S., 16 May 2019, p. 80338037. 5 p.Research output: Contribution to conference › Paper › peerreview
Open AccessFile 
Correction to "On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix"
Weiss, S., Pestana, J., Proudler, I. K. & Coutts, F. K., 1 Dec 2018, In: IEEE Transactions on Signal Processing. 66, 23, p. 63256327 3 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile19 Citations (Scopus)15 Downloads (Pure)