A trellis search algorithm for the design of FIR filters with signed-powers-of-two coefficients

An efficient two-stage algorithm is presented for designing finite-impulse response (FIR) filters that employ sums of signed-powers-of-two (SPT) coefficients. In the first stage, a prototype filter is designed using a fast time-domain approximation. This is followed, in the second stage, where the design problem is formulated as a dynamic-programming-like recursive optimization problem, by a trellis search that optimizes the filter's frequency response. The proposed search algorithm, which iteratively designs filters that employ an increasing number of SPT terms, provides a means to control the filter's implementation complexity. Design examples demonstrate that our algorithm is capable of producing filters having a better frequency response than existing methods while using fewer SPT terms. We also show that the proposed algorithm can be used to design special FIR filters such as matched transmit and receive filters employing sums of signed-powers-of-two coefficients. Also presented is a modified algorithm that further reduces the required number of adders in a filter by exploiting redundancies within the coefficients.