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Weighted least-squares approximation of FIR by IIR digital filters

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2 Author(s)
Brandenstein, H. ; Philips Semiconductors TCMC, Numberg, Germany ; Unbehauen, R.

This paper presents a method for the weighted least-squares approximation of finite impulse response (FIR) filters by infinite impulse response (IIR) filters. It is shown, how a solution to this approximation problem can be obtained by solving a related pure least-squares approximation problem. For the latter, we utilize a generalized version of a previously published technique with low computational complexity and guaranteed stability of the IIR filters. Unlike the well-established model-reduction approaches that are carried out in the state space, our method works directly with the numerator and denominator coefficients of the transfer functions. Thus, the influence of finite-precision arithmetic on the results is small. This makes our approach applicable for the approximation of large-order FIR filters and allows the usage of arbitrarily shaped weighting functions. It is shown that our method can successfully be employed to achieve a uniform approximation

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Signal Processing, IEEE Transactions on  (Volume:49 ,  Issue: 3 )