Optimal design of stable recursive digital filters by unconstrained optimization iterative updates

摘要

This paper considers the optimal design of stable recursive digital filters by using a modified Nelder-Mead simplex direct search. The filter’s denominator polynomial is expressed as a product of second-order (and a first-order section in the case of odd order denominator) sections with complex conjugate poles. In order to ensure the stability of the designed recursive digital filter, we employ a restricted range of variables on the coefficients of the filter’s denominator polynomial. This formulation can provide an option for the inclusion of a number of real poles in the filter design. Numerical examples are presented to show the performance of the proposed filter design method compared with existing methods.