Algorithmic Enhancements to Polynomial Matrix Factorisations (2019)
Abstract / truncated to 115 words
In broadband array processing applications, an extension of the eigenvalue decomposition (EVD) to parahermitian Laurent polynomial matrices - named the polynomial matrix EVD (PEVD) - has proven to be a useful tool for the decomposition of space-time covariance matrices and their associated cross-spectral density matrices. Existing PEVD methods typically operate in the time domain and utilise iterative frameworks established by the second-order sequential best rotation (SBR2) or sequential matrix diagonalisation (SMD) algorithms. However, motivated by recent discoveries that establish the existence of an analytic PEVD - which is rarely recovered by SBR2 or SMD - alternative algorithms that better meet analyticity by operating in the discrete Fourier transform (DFT)-domain have received increasing attention. While offering ... toggle 32 keywordspolynomial – matrix – eigenvalue – decomposition – PEVD – algorithms – parahermitian – paraunitary – polynomial eigenvalue – polynomial eigenvector – cross-spectral density – space-time covariance – broadband – array processing – EVD – SVD – QR – divide-and-conquer – low cost – efficient implementation – parallel processing – sequential matrix diagonalisation – SMD – second order sequential best rotation – SBR2 – laurent polynomial – dimensionality reduction – minimum-order solution – analytic – filter bank – angle of arrival – polynomial music
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