Weighted least-squares approximation of FIR by IIR digital filters

• Published in: IEEE transactions on signal processing Vol. 49; no. 3; pp. 558 - 568
• Main Authors: Brandenstein, H., Unbehauen, R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-03-2001; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Arithmetic; Computational complexity; Delay; Detection, estimation, filtering, equalization, prediction; Digital filters; Exact sciences and technology; Finite impulse response filter; Frequency; IIR filters; Impulse response; Information, signal and communications theory; Least squares method; Linear approximation; Mathematical analysis; Mathematical models; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Stability; State-space methods; Telecommunications and information theory; Transfer functions; Weighting functions; Infinite impulse response filter; Digital filter; Least squares method; Theoretical study; Signal processing; Finite impulse response filter; Frequency weighting
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.905880

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.