Sequential matrix diagonalization algorithms for polynomial EVD of parahermitian matrices

Soydan Redif, Stephan Weiss, John G. McWhirter

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

For parahermitian polynomial matrices, which can be used, for example, to characterise space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) can be generalised to a polynomial matrix EVD (PEVD). In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalisation (SMD) is introduced. At every step the SMD algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation. A proof of convergence is provided, and it is demonstrated that SMD establishes diagonalisation faster and with lower order operations than existing PEVD algorithms.
LanguageEnglish
Pages81-89
Number of pages9
JournalIEEE Transactions on Signal Processing
Volume63
Issue number1
Early online date4 Nov 2014
DOIs
Publication statusPublished - 1 Jan 2015

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Polynomials
Decomposition
Array processing

Keywords

  • parahermitian matrix
  • paraunitary matrix
  • broadband communication
  • covariance matrices
  • jacobian matrices

Cite this

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Sequential matrix diagonalization algorithms for polynomial EVD of parahermitian matrices. / Redif, Soydan ; Weiss, Stephan; McWhirter, John G.

In: IEEE Transactions on Signal Processing, Vol. 63, No. 1, 01.01.2015, p. 81-89.

Research output: Contribution to journalArticle

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