FIR filter design based on particle swarm algorithm with linear constraint

FIR filter design in frequency domain is a constrained optimal problem. The constrained problem can be changed to a non-constrained problem by introducing Lagrange multipliers. This paper optimizes the changed problem with improved particle swarm algorithm. The existing Lagrange multipliers make optimization process difficult for particle swarm algorithm. According to Lagrange duality principle, which realizes the separation of the optimization of the Lagrange multipliers, the FIR filter design of linear constrained optimal problem can be solved by particle swarm algorithm and a few iterations. Low-pass filter design proves that this method is more efficient than the standard particle swarm optimization algorithm.