Design nearly equiripple FIR filter by gradient scheme with dynamic step size

This paper proposes a gradient‐based algorithm with dynamic step size to design the nearly equiripple finite impulse response (FIR) filter, which iteratively updates the filter coefficient vector along the negative gradient direction of the peak approximation error. Moreover, besides the direction, the step size for updating is also an important parameter to be determined, and this paper proposes a dynamic method to find an appropriate step size at each round of iteration. Our results show that this dynamic step‐size scheme achieves a fast convergence rate, i.e. it can, i.e. it can design the nearly equiripple filters within a number of iterations. Specifically, by using the proposed method, the updating step size is relatively large at the early stage of iterations, which reduces the peak approximation error significantly. While, at the later stage of iterations, the updating step size becomes relatively small to approach to the equiripple solution as soon as possible. The extensive computer simulation demonstrates that the proposed algorithm outperforms the conventional algorithm in terms of the iteration number, the convergency and the performance. Copyright © 2013 John Wiley & Sons, Ltd.