Design of equiripple FIR filters with constraint using a multiple exchange algorithm

We propose a method of designing equiripple linear-phase FIR filters with linear constraint by using the Remez exchange algorithm. A novel technique is derived to convert a linearly constrained problem into an equivalent unconstrained one. We proposed a technique to modify the original desired frequency response so that the original linear constraint can be reduced to a simpler one (the null constraint) for the new target frequency response. The filter with null constraint can be designed without constraint by transformation of the original basis functions. The transformation is represented by a basis for the null space of the constraint. In this paper, we show that the transformed basis set also forms a Tchebycheff set. This fact indicates the proposed design is optimal in the Tchebycheff sense. The optimal filter is deigned by the Remez method according to the new target frequency response in transformed basis. Design examples suggest that the proposed algorithm converges fast and stably.