Shortening the order of paraunitary matrices in SBR2 algorithm

C.H. Ta, S. Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

17 Citations (Scopus)

Abstract

The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the eigenvalue decomposition to polynomial matrices, R-(z) = B(z)T(z)~B(z). However, the algorithm results in polynomials of very high order, which limits its applicability. Therefore, in this paper we evaluate approaches to reduce the order of the paraunitary matrices, either within each step of SBR2, or after convergence. The paraunitary matrix B(z) is replaced by a near-paraunitary quantity BN(z), whose error will be assessed. Simulation results show that the proposed truncation can greatly reduce the polynomial order while retaining good near-paraunitariness of BN(z).
LanguageEnglish
Title of host publication2007 6th International conference on information, communications & signal processing
Place of PublicationNew York
PublisherIEEE
Pages1396-1400
Number of pages5
ISBN (Print)9781424409822
DOIs
Publication statusPublished - 2007
Event6th Conference on Information, Communications, and Signal Processing - , Singapore
Duration: 10 Dec 200713 Dec 2007

Conference

Conference6th Conference on Information, Communications, and Signal Processing
CountrySingapore
Period10/12/0713/12/07

Fingerprint

Polynomial Matrices
Eigenvalue Decomposition
Polynomial
Diagonal matrix
Hermitian matrix
Truncation
Higher Order
Evaluate
Simulation

Keywords

  • hermitian matrices
  • polynomial matrices
  • eigenvalues
  • eigenfunctions
  • paraunitary matrices
  • SBR2 algorithm

Cite this

Ta, C. H., & Weiss, S. (2007). Shortening the order of paraunitary matrices in SBR2 algorithm. In 2007 6th International conference on information, communications & signal processing (pp. 1396-1400 ). New York: IEEE. https://doi.org/10.1109/ICICS.2007.4449828
Ta, C.H. ; Weiss, S. / Shortening the order of paraunitary matrices in SBR2 algorithm. 2007 6th International conference on information, communications & signal processing. New York : IEEE, 2007. pp. 1396-1400
@inproceedings{3dc138b84b7c455ca4fab3fa8458c364,
title = "Shortening the order of paraunitary matrices in SBR2 algorithm",
abstract = "The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the eigenvalue decomposition to polynomial matrices, R-(z) = B(z)T(z)~B(z). However, the algorithm results in polynomials of very high order, which limits its applicability. Therefore, in this paper we evaluate approaches to reduce the order of the paraunitary matrices, either within each step of SBR2, or after convergence. The paraunitary matrix B(z) is replaced by a near-paraunitary quantity BN(z), whose error will be assessed. Simulation results show that the proposed truncation can greatly reduce the polynomial order while retaining good near-paraunitariness of BN(z).",
keywords = "hermitian matrices, polynomial matrices, eigenvalues , eigenfunctions , paraunitary matrices , SBR2 algorithm",
author = "C.H. Ta and S. Weiss",
year = "2007",
doi = "10.1109/ICICS.2007.4449828",
language = "English",
isbn = "9781424409822",
pages = "1396--1400",
booktitle = "2007 6th International conference on information, communications & signal processing",
publisher = "IEEE",

}

Ta, CH & Weiss, S 2007, Shortening the order of paraunitary matrices in SBR2 algorithm. in 2007 6th International conference on information, communications & signal processing. IEEE, New York, pp. 1396-1400 , 6th Conference on Information, Communications, and Signal Processing, Singapore, 10/12/07. https://doi.org/10.1109/ICICS.2007.4449828

Shortening the order of paraunitary matrices in SBR2 algorithm. / Ta, C.H.; Weiss, S.

2007 6th International conference on information, communications & signal processing. New York : IEEE, 2007. p. 1396-1400 .

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

TY - GEN

T1 - Shortening the order of paraunitary matrices in SBR2 algorithm

AU - Ta, C.H.

AU - Weiss, S.

PY - 2007

Y1 - 2007

N2 - The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the eigenvalue decomposition to polynomial matrices, R-(z) = B(z)T(z)~B(z). However, the algorithm results in polynomials of very high order, which limits its applicability. Therefore, in this paper we evaluate approaches to reduce the order of the paraunitary matrices, either within each step of SBR2, or after convergence. The paraunitary matrix B(z) is replaced by a near-paraunitary quantity BN(z), whose error will be assessed. Simulation results show that the proposed truncation can greatly reduce the polynomial order while retaining good near-paraunitariness of BN(z).

AB - The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the eigenvalue decomposition to polynomial matrices, R-(z) = B(z)T(z)~B(z). However, the algorithm results in polynomials of very high order, which limits its applicability. Therefore, in this paper we evaluate approaches to reduce the order of the paraunitary matrices, either within each step of SBR2, or after convergence. The paraunitary matrix B(z) is replaced by a near-paraunitary quantity BN(z), whose error will be assessed. Simulation results show that the proposed truncation can greatly reduce the polynomial order while retaining good near-paraunitariness of BN(z).

KW - hermitian matrices

KW - polynomial matrices

KW - eigenvalues

KW - eigenfunctions

KW - paraunitary matrices

KW - SBR2 algorithm

U2 - 10.1109/ICICS.2007.4449828

DO - 10.1109/ICICS.2007.4449828

M3 - Conference contribution book

SN - 9781424409822

SP - 1396

EP - 1400

BT - 2007 6th International conference on information, communications & signal processing

PB - IEEE

CY - New York

ER -

Ta CH, Weiss S. Shortening the order of paraunitary matrices in SBR2 algorithm. In 2007 6th International conference on information, communications & signal processing. New York: IEEE. 2007. p. 1396-1400 https://doi.org/10.1109/ICICS.2007.4449828