Model reduction by moment matching: case study of a FIR system

We present two moment matching-based solutions to the problem of rational approximations of a finite-impulse response (FIR) system: a direct moment matching approximation performed on the FIR system and a sequential moment matching approximation performed on a block split model of a FIR system. Imposing moment matching conditions yields families of parametrized, low-order, rational approximations of the FIR filters, with guaranteed low frequency behavior. We show that the block rational implementation from [1], [2] is a particular case of the sequential moment matching result. The theory is illustrated with an example of a FIR system, where we select the free parameters such that the approximations are stable and more accurate. We compare the proposed approximations with existing rational implementations of the FIR system as well as with Loewner matrices-based approximations.