Relevance of polynomial matrix decompositions to broadband blind signal separation

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian and paraunitary matrices, strong decorrelation and spectral majorization, the PEVD and its theoretical foundations will be briefly outlined. The paper then focuses on the applicability of the PEVD and broadband subspace techniques — enabled by the diagonalization and spectral majorization capabilities of PEVD algorithms—to define broadband BSS solutions that generalise well-known narrowband techniques based on the EVD. This is achieved through the analysis of new results from three exemplar broadband BSS applications — underwater acoustics, radar clutter suppression, and domain-weighted broadband beamforming — and their comparison with classical broadband methods

Detection of Grid Voltage Anomalies via Broadband Subspace Decomposition

Due to the increase of sensitive loads on the mains power grid, measurement and monitoring of the power quality (PQ) have become an important factor for both consumers and operators. As is well-known, PQ problems occur in a very short time period with specific characteristics. In transmission or distribution systems, power quality data are collected from monitoring devices such as digital fault recorders, power quality and dynamic system monitors, etc. The recorded data has to be analysed in order to understand system anomalies. These anomalies may be due to sources of broadband noise. In this study, we employ broadband subspace decomposition, using polynomial eigenvalue decomposition, to detect these anomalies. Results demonstrate that this method may be considered as a new and effective tool for measurement and monitoring of PQ problems

Source Separation of Unknown Numbers of Single-Channel Underwater Acoustic Signals Based on Autoencoders

The separation of single-channel underwater acoustic signals is a challenging problem with practical significance. Few existing studies focus on the source separation problem with unknown numbers of signals, and how to evaluate the performances of the systems is not yet clear. We propose a solution with a fixed number of output channels to address these two problems, enabling it to avoid the dimensional disaster caused by the permutation problem induced by the alignment of outputs to targets. Specifically, we propose a two-step algorithm based on autoencoders and a new performance evaluation method for situations with mute channels. Experiments conducted on simulated mixtures of radiated ship noise show that the proposed solution can achieve similar separation performance to that attained with a known number of signals. The proposed algorithm achieved competitive performance as two algorithms developed for known numbers of signals, which is highly explainable and extensible and get the state of the art under this framework.Comment: 14 pages, 4 figures, 3 tables. For codes, see https://github.com/QinggangSUN/unknown_number_source_separatio