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

A new method is presented for optimal estimation of rational transfer function parameters to match arbitrarily-shaped frequency-domain (FD) specifications in the least-squares sense. The design is performed directly in the digital domain. The frequencies at which the specifications are given may be arbitrarily spaced. It is shown that the numerator and denominator estimation problems can be theoretically decoupled into smaller dimensional problems. The decoupled criteria retain the global optimality properties. The denominator criterion is nonlinear but possesses a weighted-quadratic structure that is utilized to formulate an iterative algorithm. Once the optimal denominator is found, the optimal numerator can be obtained by linear least-squares