Optimal frequency domain design of two-dimensional digital IIR filters

A least-squares technique is presented for designing quarter-plane separable-denominator 2-D IIR filters to best approximate prescribed frequency domain (FD) specification. It is shown that the FD error vector is linearly related to the 2-D numerator coefficients whereas the relationship with the 2-D denominators is quasi-linear. Furthermore, the numerator and denominator estimation problems are theoretically decoupled. The quasi-linear relationship is used to formulate an algorithm for iterative estimation of the denominator. The numerator is found in one step using the estimated denominator. Computer simulations show the effectiveness of the proposed method and its superior performance compared to several existing methods.