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Abstract
We investigate the singular value decomposition (SVD) of a rectangular matrix A(z) of functions that are analytic on an annulus that includes at least the unit circle. Such matrices occur, e.g., as matrices of transfer functions representing broadband multipleinput multipleoutput systems. Our analysis is based on findings for the analytic SVD applicable to continuous time systems, and on the analytic eigenvalue decomposition. Using these, we establish two potentially overlapping cases where analyticity of the SVD factors is denied. Firstly, from a structural point of view, multiplexed systems require oversampling by the multiplexing factor in order to admit an analytic solution. Secondly, from an algebraic perspective, we state under which condition spectral zeroes of any singular value require additional oversampling by a factor of two if an analytic solution is to be found. In all other cases, an analytic matrix admits an analytic
SVD, whereby the singular values are unique up to a permutation, and the left and rightsingular vectors are coupled through a joint ambiguity w.r.t.~an arbitrary allpass function. We demonstrate how some stateoftheart polynomial matrix decomposition algorithms approximate this solution, motivating the need for dedicated algorithms.
SVD, whereby the singular values are unique up to a permutation, and the left and rightsingular vectors are coupled through a joint ambiguity w.r.t.~an arbitrary allpass function. We demonstrate how some stateoftheart polynomial matrix decomposition algorithms approximate this solution, motivating the need for dedicated algorithms.
Original language  English 

Pages (fromto)  22602275 
Number of pages  16 
Journal  IEEE Transactions on Signal Processing 
Volume  72 
Early online date  11 Apr 2024 
DOIs  
Publication status  Published  8 May 2024 
Keywords
 matrix decomposition
 signal processing algorithms
 vectors
 approximation algorithms
 singular value decomposition
 indexes
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Dive into the research topics of 'On properties and structure of the analytic singular value decomposition'. Together they form a unique fingerprint.Projects
 1 Finished

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

Extraction of analytic singular values of a polynomial matrix
Khattak, F. A., Bakhit, M., Proudler, I. K. & Weiss, S., 30 Aug 2024, 32nd European Signal Processing Conference: EUSIPCO 2024. Piscataway, NJ: IEEE, p. 12971301 5 p. 1769Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book
Open AccessFile 
Paraunitary approximation of matrices of analytic functions  the polynomial procrustes problem
Weiss, S., Schlecht, S. J., Das, O. & De Sena, E., 27 Feb 2024, (Epub ahead of print) In: Science Talks. 10 p., 100318.Research output: Contribution to journal › Article › peerreview
Open AccessFile12 Downloads (Pure) 
Compact order polynomial singular value decomposition of a matrix of analytic functions
Bakhit, M. A., Khattak, F. A., Proudler, I. K., Weiss, S. & Rice, G. W., 13 Dec 2023, p. 15. 5 p.Research output: Contribution to conference › Paper › peerreview
Open AccessFile