A Model Reduction Technique for IIR Filters using Balanced Realization

In this paper, a method is proposed to reduce the order of a single-input single-output (SISO) infinite impulse response (IIR) digital filter. Since unlike IIR filters an analytical solution exists for the order reduction of FIR systems, the polynomials in the numerator and denominator of the IIR filter are regarded as FIR systems. The balanced realization technique is then applied to each polynomial separately to obtain the reduced order model. An upper bound is provided for the infinity norm of the order reduction error and conditions under which the proposed technique results in a small approximation are also discussed. Simulation results demonstrate the efficacy of the technique.