Approximation of FIR by IIR digital filters: an algorithm based on balanced model reduction

An algorithm for the approximation of finite impulse response (FIR) filters by infinite impulse response (IIR) filters is presented. The algorithm is based on a concept of balanced model reduction. The matrix inversions normally associated with this procedure are notoriously error prone due to ill conditioning of the special matrix forms required. This difficulty is circumvented here by directly formulating a reduced state-space system description which is input/output equivalent to the system that would more conventionally be obtained following the explicit step of constructing an (interim) balanced realization. Examples of FIR by IIR filter approximations are included