Design of finite wordlength IIR filters with prescribed magnitude, group delay and stability properties using simulated annealing

The problem of designing finite precision one-dimensional infinite impulse response (IIR) filters with prescribed magnitude, phase, and stability constraints is studied. The design problem is formulated as the minimization of a cost function incorporating these conflicting requirements. The first two elements of the cost function express magnitude and group delay errors between the desired and the actual frequency responses of a filter, while the third one is related to its stability margin. This cost function is minimized using simulated annealing based on the Metropolis (1953) algorithm. Examples of several finite wordlength filters designed by the above method are presented and compared with Chebyshev and elliptic filters with rounded coefficients