Optimal design of stable recursive digital filters using unconstrained optimization methods

Due to the presence of constraints on the design variables of most optimization problems, constrained optimization techniques are generally preferred to unconstrained optimization techniques in filter design. However, in the design of recursive digital filters by constrained optimization techniques, owing to the stability conditions imposed on the design, some good design values may not be considered during the optimization process. This paper presents an unconstrained optimization-based method for the optimal design of stable recursive digital filters, which reduces the customary nonlinearity added by unconstrained optimization methods. Also, an approach for generating the initial parameter vector for any set of recursive digital filter design specifications is introduced. Simulation examples for the case of a 1D transfer function are provided to illustrate the idea and performance of the method.