Space-time covariance matrix estimation: loss of algebraic multiplicities of Eigenvalues

Research output: Contribution to conferencePaperpeer-review

5 Downloads (Pure)

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 space-time 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 languageEnglish
Pages1-5
Number of pages5
Publication statusPublished - 3 Nov 2022
Event56th Asilomar Conference on Signals, Systems, and Computers - Pacific Grove, CA, United States
Duration: 30 Nov 20213 Nov 2022
https://www.asilomarsscconf.org/

Conference

Conference56th Asilomar Conference on Signals, Systems, and Computers
Abbreviated titleAsilomar'22
Country/TerritoryUnited States
Period30/11/213/11/22
Internet address

Keywords

  • space-time covariance
  • polynomial eigenvalue decomposition
  • analytic eigenvalue decomposition
  • estimation

Fingerprint

Dive into the research topics of 'Space-time covariance matrix estimation: loss of algebraic multiplicities of Eigenvalues'. Together they form a unique fingerprint.

Cite this