Weighted least-squares approximation of FIR by IIR digital filters

  • Authors:
  • H. Brandenstein;R. Unbehauen

  • Affiliations:
  • Philips Semiconductors TCMC, Numberg;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2001

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Abstract

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