Smooth QR decomposition of polynomial matrices

Faizan A. Khattak; Mohammed Bakhit; Ian K. Proudler; Stephan Weiss

Smooth QR decomposition of polynomial matrices

Faizan A. Khattak, Mohammed Bakhit, Ian K. Proudler, Stephan Weiss

Electronic And Electrical Engineering

Research output: Contribution to conference › Paper › peer-review

86 Downloads (Pure)

Abstract

This paper presents a novel algorithm for determining a compact order QR decomposition of a polynomial matrix, where both the Q and R factors themselves are approximated by polynomial matrices. The QR factorisation is subject to an allpass ambiguity; existing time domain methods can lead to factorisations of high order. The proposed algorithm performs the conventional QR decomposition the discrete Fourier transform domain. Subsequently, it establishes phase coherence between adjacent bins through a phase smoothing procedure, aimed at obtaining compact-order factors. The method is validated through experiments over an ensemble of randomized polynomial matrices and shown to outperform state-of-the-art algorithms.

Original language	English
Pages	1-5
Number of pages	5
Publication status	Published - 13 Dec 2023
Event	9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Los Suenos, Costa Rica Duration: 10 Dec 2023 → 13 Dec 2023 https://camsap23.ig.umons.ac.be/

Workshop

Workshop	9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Abbreviated title	CAMSAP
Country/Territory	Costa Rica
City	Los Suenos
Period	10/12/23 → 13/12/23
Internet address	https://camsap23.ig.umons.ac.be/

Keywords

QR decomposition
polynomial matrix
Fourier transform

Access to Document

Khattak-etal-CAMSAP-2023-Smooth-QR-decomposition-of-polynomial-matricesAccepted author manuscript, 748 KBLicence: Strath_1

Signal Processing in the Information Age (UDRC III)
Weiss, S. (Principal Investigator) & Stankovic, V. (Co-investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 31/03/24
Project: Research

Cite this

@conference{ff4de509f109450899f8577c1dceb95f,

title = "Smooth QR decomposition of polynomial matrices",

abstract = "This paper presents a novel algorithm for determining a compact order QR decomposition of a polynomial matrix, where both the Q and R factors themselves are approximated by polynomial matrices. The QR factorisation is subject to an allpass ambiguity; existing time domain methods can lead to factorisations of high order. The proposed algorithm performs the conventional QR decomposition the discrete Fourier transform domain. Subsequently, it establishes phase coherence between adjacent bins through a phase smoothing procedure, aimed at obtaining compact-order factors. The method is validated through experiments over an ensemble of randomized polynomial matrices and shown to outperform state-of-the-art algorithms.",

keywords = "QR decomposition, polynomial matrix, Fourier transform",

author = "Khattak, {Faizan A.} and Mohammed Bakhit and Proudler, {Ian K.} and Stephan Weiss",

note = "{\textcopyright} 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.; 9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP ; Conference date: 10-12-2023 Through 13-12-2023",

year = "2023",

month = dec,

day = "13",

language = "English",

pages = "1--5",

url = "https://camsap23.ig.umons.ac.be/",

}

TY - CONF

T1 - Smooth QR decomposition of polynomial matrices

AU - Khattak, Faizan A.

AU - Bakhit, Mohammed

AU - Proudler, Ian K.

AU - Weiss, Stephan

N1 - © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

PY - 2023/12/13

Y1 - 2023/12/13

N2 - This paper presents a novel algorithm for determining a compact order QR decomposition of a polynomial matrix, where both the Q and R factors themselves are approximated by polynomial matrices. The QR factorisation is subject to an allpass ambiguity; existing time domain methods can lead to factorisations of high order. The proposed algorithm performs the conventional QR decomposition the discrete Fourier transform domain. Subsequently, it establishes phase coherence between adjacent bins through a phase smoothing procedure, aimed at obtaining compact-order factors. The method is validated through experiments over an ensemble of randomized polynomial matrices and shown to outperform state-of-the-art algorithms.

AB - This paper presents a novel algorithm for determining a compact order QR decomposition of a polynomial matrix, where both the Q and R factors themselves are approximated by polynomial matrices. The QR factorisation is subject to an allpass ambiguity; existing time domain methods can lead to factorisations of high order. The proposed algorithm performs the conventional QR decomposition the discrete Fourier transform domain. Subsequently, it establishes phase coherence between adjacent bins through a phase smoothing procedure, aimed at obtaining compact-order factors. The method is validated through experiments over an ensemble of randomized polynomial matrices and shown to outperform state-of-the-art algorithms.

KW - QR decomposition

KW - polynomial matrix

KW - Fourier transform

M3 - Paper

SP - 1

EP - 5

T2 - 9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing

Y2 - 10 December 2023 through 13 December 2023

ER -

Smooth QR decomposition of polynomial matrices

Abstract

Workshop

Keywords

Access to Document

Fingerprint

Projects

Signal Processing in the Information Age (UDRC III)

Cite this