Smooth QR Decomposition of Polynomial Matrices
- Resource Type
- Conference
- Authors
- Khattak, Faizan A.; Bakhit, Mohammed; Proudler, Ian K.; Weiss, Stephan
- Source
- 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2023 IEEE 9th International Workshop on. :76-80 Dec, 2023
- Subject
- Bioengineering
Computing and Processing
Signal Processing and Analysis
Smoothing methods
Conferences
Discrete Fourier transforms
Coherence
Approximation algorithms
Matrix decomposition
Time-domain analysis
- Language
This paper presents a novel algorithm for determining a compact order QR decomposition of a polynomial matrix, where both the $\mathrm{Q}$ and $\mathrm{R}$ 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.