An improved iterative design for powers-of-two coefficient FIR filters

An iterative design technique for sum of powers-of-two (SOPOT) coefficient filters which uses two complementary filters in cascade is developed. These filters are designed to equalize each other's errors in the frequency domain, and thus when cascaded yield near-optimum frequency response. The technique is universal in the sense that it can be used to design filters in the minimax or the least-square-error sense. The initial SOPOT coefficients for the complementary filters are obtained by simple rounding to SOPOT values from an optimum real coefficient design. A localized search scheme is used to adjust the response of each of the filters such that the overall error from the ideal design is minimized. This process is repeated until convergence is reached. The cascaded complement design not only provides error equalization, but it also brings the SOPOT coefficients closer to optimum real values due to the convolution taking place between coefficients in the cascaded model.<>