Optimal design of digital IIR filters by model-fitting frequency response data

A new frequency-domain (FD) approach is presented for optimal estimation of rational transfer functions coefficients. The proposed method seeks to match any arbitrarily-shaped FD specifications in the least-squares sense. The desired specifications may be arbitrarily spaced in frequency. The design is performed directly in the digital domain, and no analog to digital transformation is necessary. The proposed method makes use of the inherent mathematical structure in this rational modeling problem to theoretically decouple the numerator and denominator estimation problems into two lower dimensional problems. The denominator criterion is nonlinear but possesses a weighted-quadratic structure, which is convenient for iterative optimization. The optimal numerator is found linearly by solving a set of simultaneous equations. The decoupled criteria retain the global optimality properties. The performance of the algorithm is demonstrated with some simulation examples. >

[1]  Edward J. Wegman,et al.  Statistical Signal Processing , 1985 .

[2]  L. Mcbride,et al.  A technique for the identification of linear systems , 1965 .

[3]  Ramdas Kumaresan,et al.  Identification of rational transfer function from frequency response sample , 1990 .

[4]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[5]  E. C. Levy.  Complex-curve fitting , 1959, IRE Transactions on Automatic Control.

[6]  N. Levinson.  The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction , 1946 .

[7]  R. Kumaresan.  Parameter Estimation of Signals Corrupted by Noise Using a Matrix of Divided Differences , 1989 .

[8]  Ramdas Kumaresan.  On a frequency domain analog of Prony's method , 1990, IEEE Trans. Acoust. Speech Signal Process..

[9]  Arnab K. Shaw.  Optimal identification of discrete-time systems from impulse response data , 1994, IEEE Trans. Signal Process..

[10]  T. Hinamoto,et al.  Design of 2-D separable-denominator recursive digital filters , 1984 .

[11]  Ramdas Kumaresan,et al.  Fitting a pole-zero filter model to arbitrary frequency response samples , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[12]  Arnab K. Shaw.  An optimal method for identification of pole-zero transfer functions , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[13]  C. K. Yuen,et al.  Digital Filters , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  L. Jackson.  Digital filters and signal processing , 1985 .

[15]  A. Evans,et al.  Optimal least squares time-domain synthesis of recursive digital filters , 1973 .

[16]  J. Cadzow.  Recursive digital filter synthesis via gradient based algorithms , 1976 .

[17]  R. Roberts,et al.  The use of second-order information in the approximation of discreate-time linear systems , 1976 .

[18]  C. Burrus,et al.  Time domain design of recursive digital filters , 1970 .

[19]  J. L. Hock,et al.  An exact recursion for the composite nearest‐neighbor degeneracy for a 2×N lattice space , 1984 .

[20]  Leonard Weiss,et al.  Prony’s Method, Z-Transforms, and Padé Approximation , 1963 .

[21]  Arnab K. Shaw.  A decoupled approach for optimal estimation of transfer function parameters from input-output data , 1994, IEEE Trans. Signal Process..

[22]  E. Miller,et al.  Pole extraction from real-frequency information , 1980, Proceedings of the IEEE.

[23]  Arnab K. Shaw.  Design of denominator separable 2-D IIR filters , 1995, Signal Process..

[24]  B. Friedlander,et al.  The Modified Yule-Walker Method of ARMA Spectral Estimation , 1984, IEEE Transactions on Aerospace and Electronic Systems.

[25]  F. B. Hildebrand,et al.  Introduction To Numerical Analysis , 1957 .

[26]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[27]  Arye Nehorai.  A minimal parameter adaptive notch filter with constrained poles and zeros , 1985, IEEE Trans. Acoust. Speech Signal Process..