Scaled CR-(RC)n Digital Filter Design for Precision Pulse Processing in Spectroscopy Applications

Digital pulse processing systems have become crucial in a wide range of scientific, industrial, and medical applications, particularly in the context of spectroscopy. This paper presents a novel approach to pulse shaping for gamma-ray and x-ray spectroscopy using a combination of CR and RC filters in digital signal processing. The proposed design aims to overcome challenges associated with exponential decay inputs and introduces a scaling factor to achieve a consistent amplitude scale in the filtered output. Specifically, the design tackles the issue of undershoot arising from exponential decay inputs, a significant limitation in existing CR-RC filter implementations. This is achieved through a novel post-processing step. This conversion ensures clean, semi-Gaussian pulse shapes free from distortion, leading to improved accuracy in subsequent analysis. Furthermore, the proposed approach introduces a scaling factor that guarantees a consistent 1-to-1 ratio between input and output amplitudes. This unique feature simplifies subsequent signal processing pipelines and ensures accurate energy measurements, crucial for spectroscopic applications. The effectiveness of this novel method is demonstrated through experimental evaluations using real data acquired from an HPGe detector. The experimental results successfully demonstrate the correction of undershoot and a consistent 1-to-1 ratio between input and output amplitudes, validating the effectiveness of the proposed method in enhancing the accuracy of digital pulse shaping systems in spectroscopy.