Mathematical Tools for Processing Broadband Multi-Sensor Signals
Stephan Weiss · Proceedings of the World Congress on Electrical Engineering and Computer Systems and Science · 2020
Spatial information in broadband array signals is embedded in the relative delay with which sources illuminate different sensors.Therefore, second order statistics, on which cost functions such as the mean square rest, must include such delays.Typically, a space-time covariance matrix therefore arises, which can be represented as a Laurent polynomial matrix.The optimisation of a cost function then requires extending the utility of the eigenvalue decomposition from narrowband covariance matrices to the broadband case of operating in a space-time covariance matrix.This overview paper summarises efforts in performing such factorisations, and demonstrated via the exemplar application of a broadband beamformer how thus well-known narrowband solutions can be extended to the broadband case using polynomial matrices and their factorisations.