Efficient design of FIR filters with minimum filter orders using l0-norm optimization

In this paper, a novel method is proposed to design FIR filters with minimum orders. The original design problem is formally expressed as an l₀-norm optimization problem. An iterative procedure is developed to solve this problem. Although, for a set of given specifications, the proposed method is not guaranteed to find the optimal solution, one can greedily decrease the filter order until the specifications cannot be further satisfied. Simulation results demonstrate that the greedy search needs a limited number of iterations, and the overall computational complexity is not too high. Compared to the classical estimation methods, the proposed method can be utilized for general design specifications. The performance of the proposed design method can be verified by a large number of simulations.