A Lattice Structure Optimization Method and Sensitivity Analysis of Finite Impulse Response Filter
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摘要: 有限脉冲响应(FIR)滤波器是无线通信研究中多载波调制系统的主要组成单元。针对有限字长效应导致FIR滤波器性能下降问题，该文提出一种FIR滤波器格型结构改善因量化导致的滤波器系数误差，即降低系数灵敏度，利用状态空间结构表示相应改进格型结构系数，并推导分析其系数灵敏度表达式。仿真实例验证理论推导结果，即改进格型结构系数灵敏度与采样周期相关。与传统格型结构相比，在量化字长和采样周期约束下，改进格型结构频响特性曲线更接近理想频响特性曲线，系数灵敏度更小，抗有限字长效应能力更好。Abstract: Finite Impulse Response(FIR) filter is the main component of multi-carrier modulation system in wireless communication research. Considering the problem of FIR filter performance degradation caused by the finite word length effect, an FIR filter lattice structure is proposed to optimize the filter coefficient error caused by quantization, that is, to reduce the coefficient sensitivity. The state space structure is used to express the corresponding improved lattice structure coefficients, and the coefficient sensitivity expression is derived and analyzed. The simulation results show that the sensitivity of the improved lattice structure coefficient is related to the sampling period. Compared with the traditional lattice structure, under the constraints of quantization word length and sampling period, the frequency response characteristic curve of the improved lattice structure is closer to the ideal frequency response characteristic curve, the coefficient sensitivity is smaller, and the ability of resisting finite word length effect is better.
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表 2 两种结构幅频响应与理想幅频响应的差值
字长Bc (bit) 采样周期Ts (s) ωRz (dB) ωRρ (dB) 8 10–2 4.9703 2.9412 10–3 4.9703 0.9399 10–4 4.9703 0.9437 10 10–2 4.6208 0.5500 10–3 4.6208 0.1509 10–4 4.6208 0.1244 16 10–2 4.7135 0.0018 10–3 4.7135 9.1602×10–4 10–4 4.7135 3.9264×10–4 
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