Designing linear phase IIR filters from FIR prototypes

Linear phase IIR filters can be designed from FIR prototypes by using standard model reduction techniques. These techniques are based upon obtaining a balanced realization of the original system, and then removing the weakly controllable and observable states. Some standard model reduction techniques are explored as well as an extension to discrete time of a previously proposed continuous time frequency weighting technique. The techniques are applied to the design of two example filters. In both cases, the new frequency weighting technique produces a lower order filter, at the cost of increased ripple in the pass-band group delay