Iterative Linear Programming Design of Digital Lowpass FIR Filters with Linear Phase

The minimax optimization is widely used in wireless communications to design the equiripple lowpass filter, such as the Linear Programming (LP) method. However, the conventional LP method suffered from its large computation loads. Hence, this study investigates an iterative LP method, in which constraints are iteratively thrown on the non-uniformly distributed frequency grid to reduce the problem scale as much as possible, resulting in much lower computations. Moreover, since the non-uniform frequency grid allows us to precisely control the ripple, the proposed method also yields a better equiripple result compared to the conventional LP method and the Particle Swarm Optimization (PSO) algorithm.