基于L_0范数约束非相邻系数FIR数字滤波器设计

Design of FIR Filter with Non-Adjacent Coefficient Based on L_0-Norm Constraint

传统有限冲击响应滤波设计时,均默认滤波器系数相邻。该文提出了采用L0范数约束的非相邻系数有限冲击响应滤波器设计模型,保持其线性相位特性,通过增加滤波器设计的自由度,以少量的系统延时为代价来提高滤波器性能。并采用遗传算法来解该非凸优化模型,进一步推导出近似解的求解方法,降低了算法复杂度。计算机仿真结果表明,在相同的阶数下,该滤波器模型较传统模型有更小的逼近误差。

For traditional finite-impulse-response （FIR） filter, designers usually default to that the coefficient should be adjacent. In this paper, we propose a new model of the FIR filter based on the L0-norm, which improves the performance of FIR filter by increasing few delays and keeps the linear phase at the same time. Genetic algorithm is proposed to solve the proposed non-convex optimization model. An approximate solution is derived based on the result of genetic algorithm to reduce the computational burden. Computer simulation results demonstrate its lower approximation error compared with traditional FIR filters with the same filter order.