Design of Linear Phase FIR Filters With High Probability of Achieving Minimum Number of Adders

In this paper, an algorithm is proposed for the design of low complexity linear phase finite impulse response (FIR) filters with optimum discrete coefficients. The proposed algorithm, based on mixed integer linear programming (MILP), efficiently traverses the discrete coefficient solutions and searches for the optimum one that results in an implementation using minimum number of adders. During the searching process, discrete coefficients are dynamically synthesized based on a continuously updated subexpression space and, most essentially, a monitoring mechanism is introduced to enable the algorithm's awareness of optimality. Benchmark examples have shown that the proposed algorithm can, in most cases, produce the optimum designs using minimum number of adders for the given specifications. The proposed algorithm can be simply extended for the optimum design with the maximum adder depth constraint.