Gaussian signals have symmetry and completeness, hence, the Gaussian filtering method is widely used in nuclear signal processing and radiation energy spectrum analysis. The mathematical description of Gaussian signals is relatively complex, which makes it difficult to construct digital Gaussian pulse shaping filters for nuclear pulse signal real-time processing. The commonly used digital quasi-Gaussian shaping algorithm in radiation measurement systems is derived from the differential equations of Sallen-Key and CR-(RC)n filters in analog nuclear electronics. However, its output shaping pulse signals have poor symmetry and problems such as undershoot occur when used in a single stage.
This study aims to explore the convolutional quasi-Gaussian pulse shaping filter algorithm and apply it to the processing of X-ray fluorescence measurement system experimental platform to obtain measured nuclear pulse data.
Firstly, a convolutional quasi-Gaussian pulse shaping algorithm was implemented based on trapezoidal pulse signals, and bipolar pulse shaping was achieved after the initial convolution. Then, the second convolution was accumulated and summed to obtain left and right symmetric quasi-Gaussian shaping pulses. The digital recursive formula of the quasi-Gaussian pulse shaping algorithm was obtained using the Z-transform method, and the effectiveness of the algorithm and the influence of shaping parameters on the amplitude frequency characteristics were studied through simulation. Finally, quasi-gaussian shaping algorithm and trapezoidal shaping algorithm were applied separately to the offline process of measured nuclear pulse data from the X-ray fluorescence measurement system experimental platform.
The quasi-Gaussian pulse shaping filter has better high-frequency noise suppression performance compared to trapezoidal pulse shaping filters. With the increase of the values of shaping parameters na and nc, the filter passband decreases whilst the low-frequency amplitude relatively increases, and the high-frequency noise suppression effect is enhanced. However, this also leads to shaping pulse broadening and increases the probability of pulse pile-up.
The experimental results demonstrate that the quasi-Gaussian pulse shaping algorithm has better pile-up pulse separation ability. Under identical X-ray tube voltage and current conditions and peaking time, the energy resolution of the energy spectra obtained by both algorithms is fundamentally equivalent. However, the energy spectrum with quasi-Gaussian pulse shaping has a higher characteristic peak area.
