Applications of polynomial eigenvalue decomposition to multichannel broadband signal processing: part 2: eigenvalue decomposition

Multichannel broadband signals arise at the core of many essential military technologies such as radar, sonar and communications, and commercial applications like telecommunications, speech processing, healthcare monitoring and seismic surveillance. The success of these applications often depends on the performance of signal processing tasks such as source localization, channel coding, signal enhancement, and source separation. U n multichannel broadband arrays or convolutively mixed signals, the array signals are generally correlated in time across different sensors. Therefore, the time delays for broadband signals cannot be represented by phase shift alone but need to be explicitly modelled. The relative time shifts are captured using the polynomial space-time covariance matrix, where decorrelation over a range of time shifts can be achieved using a polynomial EVD (PEVD). This tutorial is dedicated to recent developments in PEVD for multichannel broadband signal processing applications. We believe this tutorial and resources, such as code and demo webpages, will motivate and inspire many colleagues and aspiring PhD students working on broadband multichannel signal processing to try PEVD. The applications and demonstrations covered in this proposed tutorial include direction of arrival estimation, beamforming, source identification, weak transient detection, voice activity detection, speech enhancement, source separation and subband coding.