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