An Improvement Project of Roundoff Noise Performance of FIR Filters Based on Structure Optimization
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摘要:
针对滤波器组系统硬件实现时原型滤波器的有限字长效应问题，该文研究如何改善FIR原型滤波器由信号量化引起的舍入噪声，即降低舍入噪声增益，提出一种FIR滤波器优化结构。通过分析舍入噪声来源，利用多项式参数化方法对舍入噪声增益表达式进行推导。仿真实例证明，在不同字长约束条件下所提结构滤波器的幅频相频响应与理想状态基本吻合；通过与现有算法对比，所提结构具有较小的舍入噪声增益。
Abstract:For the problem of the finite word length effect of prototype filters in hardware implementation of the filter bank system, this paper studies how to improve the performance of roundoff noise caused by signal quantization for the FIR prototype filter, that is, to reduce the roundoff noise gain. An FIR filter optimization structure is proposed. By analyzing the source of roundoff noise, a polynomial parameterization method is used to derive the roundoff noise gain expression. The simulation example shows that the amplitude-frequency and phase-frequency response of the proposed structure filter are basically consistent with the ideal state under different constraint of word length. Compared with the existing algorithms, the proposed structure has a smaller roundoff noise gain.
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Key words:
- FIR filter /
- Finite word length /
- Roundoff noise gain
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表 1 低通滤波器仿真参数
参数 数值 通带截止频率 $0.3{{π}}\ {\rm{rad}}$ 阻带截止频率 $0.5{{π}}\ {\rm{rad}}$ 通带最大衰减 1 dB 阻带最小衰减 40 dB 
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表 2 各结构舍入噪声增益性能对比
自由因子$K$ ${10^{ - 7}}$ ${10^{ - 6}}$ ${10^{ - 5}}$ ${10^{ - 4}}$ ${10^{ - 3}}$ 优化结构 $6.248$ $6.248$ $6.248$ $8.425$ $10.210$ 传统结构 $24$ $24$ $24$ $24$ $24$
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