This article is devoted to the polynomial eigenvalue decomposition (PEVD) and its applications in broadband multichannel signal processing, motivated by the optimum solutions provided by the EVD for the narrowband case [1], [2]. In general, we would like to extend the utility of the EVD to also address broadband problems. Multichannel broadband signals arise at the core of many essential commercial applications, such as telecommunications, speech processing, health-care monitoring, astronomy and seismic surveillance, and military technologies, including radar, sonar, and communications [3]. The success of these applications often depends on the performance of signal processing tasks, including data compression [4], source localization [5], channel coding [6], signal enhancement [7], beamforming [8], and source separation [9]. In most cases and for narrowband signals, performing an EVD is the key to the signal processing algorithm. Therefore, this article aims to introduce the PEVD as a novel mathematical technique suitable for many broadband signal processing applications.

中文翻译：

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多通道宽带信号处理的多项式特征值分解：一种提供新见解和解决方案的数学技术


本文致力于多项式特征值分解 (PEVD) 及其在宽带多通道信号处理中的应用，其动机是 EVD 为窄带情况提供的最佳解决方案 [1]、[2]。总的来说，我们希望扩展 EVD 的用途来解决宽带问题。多通道宽带信号是许多重要商业应用的核心，例如电信、语音处理、医疗保健监测、天文学和地震监测以及军事技术，包括雷达、声纳和通信 [3]。这些应用的成功通常取决于信号处理任务的性能，包括数据压缩[4]、源定位[5]、信道编码[6]、信号增强[7]、波束成形[8]和源分离[9] ]。在大多数情况下，对于窄带信号，执行 EVD 是信号处理算法的关键。因此，本文旨在介绍 PEVD 作为一种适用于许多宽带信号处理应用的新型数学技术。