Design of nearly optimum power-of-two coefficient cascaded filters

A design technique is developed for powers-of-two coefficient FIR filters that use two complementary filters in cascade. The two filters are designed to cancel out each other´s errors in the frequency domain. Since the cascaded design results in a convolution of the individual filter´s power-of-two coefficients, the combined filter´s coefficients are much closer to the optimum real coefficients thus yielding a near optimum frequency response. The powers-of-two coefficients for the first filter are obtained by simple rounding from an optimal real coefficient design, and a localized search scheme is used for its cascaded complement. The design technique allows the desired frequency response to be approximated in the least square or the minimax sense