Least-squares approximation of FIR by IIR digital filters

In this paper, an algorithm is presented for the least-squares approximation of FIR filters by IIR filters. The algorithm is an iterative procedure where each iteration requires the solution of an overdetermined set of linear equations and some digital filtering operations. All calculations are performed with the numerator and denominator coefficients of the transfer functions. A conversion to state-space descriptions is not necessary. Examples show that the approximation error is as small as that of the IIR filters obtained with balanced model reduction. Moreover, the effects of numerical errors are negligible. Thus, our algorithm is applicable even in cases where the FIR filter length is large.