Order Reduction of Multi-Channel FIR Filters by Balanced Truncation

Modern digital signal processing increasingly leverages multi-channel systems and algorithms to tackle emerging challenges, e.g., in beamforming, crosstalk cancellation (CTC) or active noise control. Commonly, the modeling, design and simulation of these systems involves the use of multiple-input multiple-output (MIMO) finite impulse response (FIR) filters. To increase the practical feasibility, these potentially resource-intensive FIR filters can be approximated by infinite impulse response (IIR) filters of lower order. Balanced truncation (BT) can be used for the approximation, but is not used as widely in these areas. A possible reason for this is the state space formulation of the algorithm, which does not scale well for general systems of high order. In this contribution, we present a BT algorithm which is specifically tailored to the approximation of MIMO FIR filters which avoids most of the usually needed computations. This algorithm can be applied to a number of current problems and we study two examples in detail. We find the numerical accuracy to be satisfactory even with high-order systems.