Multiplicative linear phase FIR filters

A linear phase MFIR realization of a desired frequency response magnitude is shown to require multipliers and adders, where N is the order of the minmax FIR design of and n of the IIR design of . Lowpass filters are used as the basis of our computational comparison. Frequency response error bounds are found and roundoff noise properties considered. The optimal ordering for minimum roundoff noise output is found for a class of MFIR filters. Several design examples are considered and their computational efficiency compared to direct optimal designs. Other applications are suggested. In particular, comb filters are shown to have an exact MFIR realization.