Design of cascade-form IIR filters with powers-of-two coefficients using mixed integer linear programming

We propose an optimal design method for digital IIR filters with powers-of-two coefficients. This method is based upon the formulation of a linear optimization problem that minimizes the filter's complexity for given specifications. It is shown that by taking the logarithm to the transfer function of cascade-form IIR filters, the design problem becomes linear and can be solved by mixed integer linear programming (MILP). Design examples are presented to demonstrate the efficiency of the proposed method.