任意噪声和约束下的最佳数字滤波器设计

Optimum digital filter synthesis with arbitrary constraints and noise

为提高数字谱仪的能量分辨率,利用约束最优化方法提出了一个在任意平稳噪声背景下直接设计最佳数字有限冲击响应(FIR)滤波器的方法。该方法易于附加任意时域和频域约束(平顶、基线恢复等)。详细给出了最佳滤波器的设计推导过程,并在设计实例基础上,分析了滤波器的时域、频域响应和不同约束条件下的最大信噪比曲线。结果证明,该方法能够有效去除基线漂移和弹道亏损,得到了约束条件下的最大信噪比,适合在未知系统噪声特性情况下的高计数率、高精度谱仪中使用。

The energy resolution of digital spectroscopy can he improved by finite impulse response （FIR） filters optimized for the presence of any kind of stationary noise. The designs were optimized using the constrained optimization technique with arbitrary time domains and frequency domain constraints （fiat-top, baseline restorer, etc. ）. Synthesis results for a typical example were analyzed in both the time and frequency domains to investigate the maximum signal-to-noise ratio （SNR） for various constraints. The filter effectively removes baseline drift and ballistic deficit, while possibly achieving the maximum SNR. The results show that the method is suitable for high-speed, high-resolution digital spectroscopy, especially when the noise characteristics are unknown.