Two-dimensional IIR filter design with magnitude and phase error criteria

Two-dimensional IIR filters are designed using an error criterion consisting of the weighted sum of magnitude, phase, and stability errors, thereby extending the spectral factorization-based method to complex approximation. The weights are adjusted to effectively constrain stability while minimizing a weighted sum of frequency domain magnitude and phase errors. We use a derivative-free variant of the Marquardt optimization algorithm augmented by a one-dimensional search. We present examples of approximation of both linear and nonlinear phase ideal transfer functions, and conduct comparisons across a range of numerator and denominator orders, from FIR to all-pole, while keeping the total number of coefficients approximately constant. We find that the designed IIR filters offer better magnitude response in the case of linear phase ideal functions, even considering coefficient reflection symmetry, but of course, the FIR filter has the better (zero) phase error. When the ideal transfer function has nonlinear phase, and hence no coefficient reflection symmetry, we find that the designed IIR filter can perform better than the FIR filter with regard to both magnitude and phase error, when magnitude error is weighted more heavily than phase error.

[1]  M. Ekstrom,et al.  Two-dimensional recursive filter design--A spectral factorization approach , 1980 .

[2]  G. Garibotto,et al.  2-D recursive phase filters for the solution of two-dimensional wave equations , 1979 .

[3]  J. W. Woods,et al.  2-D direct form, recursive filter design with magnitude and phase specifications , 1981, ICASSP.

[4]  M. Ekstrom,et al.  Two-dimensional spectral factorization with applications in recursive digital filtering , 1976 .

[5]  J. Dennis,et al.  Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation , 1971 .

[6]  M. Fahmy,et al.  Design of two-dimensional recursive digital filters with specified magnitude and group delay characteristics , 1978 .

[7]  David B. Harris.  Design of stable all-pass filters , 1979, ICASSP.

[8]  M. Ekstrom,et al.  Realizable Wiener filtering in two dimensions , 1982 .

[9]  Jake K. Aggarwal,et al.  The measurement of phase distortion due to filtering in digital pictures , 1977 .

[10]  Thomas S. Huang,et al.  The importance of phase in image processing filters , 1975 .

[11]  M. Fahmy,et al.  Symmetry exploitation in the design and implementation of recursive 2-D rectangularly sampled digital filters , 1981 .

[12]  Graham A. Jullien,et al.  Designing near linear phase recursive filters using linear programming , 1977 .

[13]  K. Peacock,et al.  On the practical design of discrete velocity filters for seismic data processing , 1982 .