A Non-Monotone Optimization Algorithm for IIR Filter Design

In this paper, a new algorithm is proposed for digital filter design. Filter specifications are fixed as a mask defined by upper and lower bounds on the magnitude response of the filter. The filter is designed by minimizing a particular objective function measuring the average violation on mask constraints for a discrete set of frequencies. The minimization of the objective function is performed by a non monotone modification of the projected gradient algorithm. It allows to include the filter stability constraints in the optimization problem, while the non monotone approach avoids the local minima problem which is often encountered in non convex optimization problems.