Digital Filter Order Reduction

Abstract

In this paper, a method is proposed to reduce the order of IIR filters by means of control theory. Using the state space representation of the filter and the controllability and observability gramians of a FIR filter in a closed form, balanced realization method is used to reduce the order of the filter. For IIR filters, long division is used first to find a FIR model for the filter. The balanced realization technique is then utilized to find the reduced order model for the resultant FIR model used to approximate the IIR filter. The reduced-order model obtained for IIR filter consists of the approximation errors in both balanced realization procedure, as well as the long division process. A method is given to obtain an upper bound for the infinity norm of error between the original IIR filter and the FIR model derived from the long division. A bound on the norm of the overall approximation error is then obtained by adding the long division error to the model reduction error of balanced realization.