低灵敏度FIR滤波器优化结构  

FIR filter optimal structure with low sensitivity

作　　者：庄陵[1] 唐园园 ZHUANG Ling;TANG Yuanyuan(School of Communication and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆邮电大学通信与信息工程学院,重庆400065

出　　处：《华中科技大学学报（自然科学版）》2021年第1期55-62,共8页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：重庆市科委资助项目(cstc2017shmsA130115)。

摘　　要：针对有限冲激响应(FIR)滤波器实现时因有限精度限制导致滤波器性能下降问题,基于连续时间传递函数,利用增量差分离散方法提出一种低灵敏度FIR滤波器优化结构.首先,根据传统z算子与增量差分Delta算子的关系,利用双线性变换求得模拟域离散后的状态空间实现,并将系数矩阵进行稀疏化分解得到优化结构状态空间实现;然后,采用状态空间法分析优化结构的参数灵敏度,推导灵敏度和舍入噪声增益表达式;最后,比较各结构实现复杂度,利用数值实例分析灵敏度与舍入噪声性能,并在不同采样周期和量化字长下得到滤波器的幅频与相频响应,将其与理想频响特性进行对比.仿真实验结果表明:所提优化结构的系数灵敏度随着采样频率增加逐渐减小,且在有限字长约束下,幅频和相频响应更稳定.Aiming at the performance degradation caused by the finite precision limitation in finite impulse response(FIR) filter implementation,based on the continuous time transfer function,a FIR filter optimal structure with low sensitivity was proposed by using the incremental difference discrete method.First,according to the relationship between traditional z-operator and delta operator,the state space realization of discrete simulation domain was obtained by bi-linear transformation,and the state space realization of optimized structure was obtained by sparse decomposition of coefficient matrix.Then,parameter sensitivity of the optimized structure was analyzed by state space method,sensitivity expression was derived,and expression of rounding noise gain was derived.Finally,after comparing the implementation complexity of each structure,numerical examples were used to analyze the sensitivity and rounding noise performance,and the amplitude frequency and phase frequency responses of the filter were obtained under different sampling periods and quantization word length.The comparison and analysis were made between the amplitude frequency response and the ideal frequency response characteristics.Simulation results show that the coefficient sensitivity of the optimized structure decreases with the increase of sampling frequency,and the amplitude-frequency and phasefrequency responses are more stable under the constraint of finite word length.

关 键 词：有限冲激响应(FIR) 数字滤波器 状态空间 有限字长 灵敏度 频响特性 

分 类 号：TN713.7[电子电信—电路与系统]