In order to improve noise filtering for high-resolution X-ray spectroscopy using silicon drift detectors, optimum finite impulse response filters are calculated and tested experimentally. Common matched filter theory cannot be applied for this problem since the filters need to fulfill several requirements regarding their time domain transfer function, like, for example, the presence of a flat-top, zero-filter area. Therefore, the utilization of digital penalized least mean square method with silicon drift detectors is presented. Adaptations to the method are applied in order to suit the considered application targeting low dead-time at high count rates using modern silicon drift detectors with fast charge amplifiers. The workflow for filter calculation is presented: Signal data are acquired using a spectroscopy setup in order to obtain pulse shape and noise information. Desired constraints regarding the time-domain transfer function of the filters are written out, and limits for the precision of their fulfillment are derived. Optimization is carried out, and resulting filters are presented. In order to experimentally test the calculated filters, implementation in hardware is done. ⁵⁵Fe spectra are acquired and evaluated. Noise reduction is rated by calculation of residual electronic noise in the recorded ⁵⁵Fe spectra. Comparison to the noise reduction of trapezoid filters is done. Improvement up to (5.2 ± 0.3)% was found using the calculated optimum filter, proving the successful utilization of digital penalized least mean square method for signal processing with modern silicon drift detectors.

中文翻译：

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硅漂移探测器信号处理的最佳滤波器设计

为了改进使用硅漂移探测器的高分辨率 X 射线光谱的噪声过滤，计算并通过实验测试了最佳有限脉冲响应滤波器。常见的匹配滤波器理论不能应用于这个问题，因为滤波器需要满足关于它们的时域传递函数的几个要求，例如，平顶、零滤波器区域的存在。因此，提出了在硅漂移检测器中使用数字惩罚最小均方方法。对该方法进行了调整，以适应所考虑的应用，目标是使用具有快速电荷放大器的现代硅漂移检测器在高计数率下实现低死区时间。过滤器计算的工作流程如下：使用光谱设置获取信号数据，以获得脉冲形状和噪声信息。写出有关滤波器时域传递函数的所需约束，并推导出其实现精度的限制。执行优化，并呈现结果过滤器。为了对计算出的滤波器进行实验测试，在硬件中实现。获得并评估了^{55 个}Fe 光谱。降噪是通过计算记录的⁵⁵ Fe 光谱中的残余电子噪声来评定的。与梯形滤波器的降噪比较完成。使用计算出的最佳滤波器发现了高达 (5.2 ± 0.3)% 的改进，证明了数字惩罚最小均方方法在现代硅漂移检测器的信号处理中的成功利用。