A simple algorithm for constrained least square design for FIR filters

In this paper, a new design algorithm of FIR filters is proposed based on the following two notions in filter design. Firstly, only cutoff frequency is defined without specifying the transition bands. Secondly, equiripple filters and best L₂ filters are optimum in terms of the Chebyshev criteria (minimum peak error) and L₂ criteria (least squared error), respectively. However, with only a slight penalty of performance under one criterion, performance under the other criterion can be significantly increased. Motivated by these two notions, the proposed algorithm uses the steepest gradient descent (SGD) algorithm to correct the coefficients of optimum L₂ filters iteratively to achieve the optimum result. Simulation results show that the proposed algorithm has a comparable performance to the optimum algorithm while at a lower complexity as well as to avoid some divergent problems