Application and characterization of digital Sallen-Key filter in nuclear spectrum smoothing

Abstract

In the nuclear spectrum analysis processing, spectrum smoothing can remove the statistical fluctuation in the spectrum, which is beneficial for peak detection and peak area calculation. In this work, a spectrum smoothing algorithm is proposed based on digital Sallen-Key filter, which contains four parameters (m, n, k, D). The amplitude-frequency response curve of Sallen-Key filter is deduced and the filtering performance is analyzed. Meanwhile, the effects of the four parameters on the shape of the smoothed spectrum are explored: D affects the counts and peak areas of the spectrum, and the peak area can be corrected by the peak area correction function S'. The parameters of m, n and k affect the peak position after smoothing, making the peak position shift to the right, and the peak position correction function P' can be used to correct the peak position, when n¿2, the spectrum data appear negative after smoothing, when k¿2, the smoothed spectrum broadening degree is greater than 20%. Smoothness (R), noise smoothing factor (NSF), spectrum count ratio before and after smoothing (PER), and comprehensive evaluation factor (Q) are used to evaluate the smoothing effect of the algorithm. The parameters of the algorithm are optimally selected: about the gamma spectrum of ¹³⁷Cs and ⁶⁰Co, the optimal parameters are m=1.5 n=2 k=2 D=1, about the characteristic X-ray spectrum of Fe and quasi-geological sample (TiMnFeNiCuZn), the optimal parameters are m=1.1 n=1.1 k=1.3 D=1. Based on Sallen-Key smoothing method, Fourier transform method, Gaussian function method, wavelet transformation method, center of gravity method and least squares method, the gamma spectrum of ¹³⁷Cs is smoothed and denoised in this paper. The results show that the Sallen-Key method has better spectrum denoising effect (R=0.6056) and comprehensive performance indicators (Q=0.6104), which can be further applied for the smoothing of nuclear spectrum data.

Keywords: Digital Sallen–Key filters; Parameter optimization; Smoothness; Spectrum smoothing.