An efficient iterative algorithm for designing optimal recursive digital filters

A new iterative algorithm is presented for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the finite impulse response (FIR) filter design algorithm of McClellan et al. as a subroutine. As a consequence, the entire design procedure proves to be very efficient. The approach taken also permits the filter to be designed with a desired (passband-to-stopband) ripple ratio. Typically, the design algorithm converges to the optimal solution within a few iterations. Several examples are given to illustrate the procedure. The filter design computer program is provided in the Appendix.