On the analysis of signal peaks in pulse-height spectra

TL;DR

This paper compares three analysis methods for peak detection in pulse-height spectra, highlighting their advantages and limitations in different noise and shape conditions.

Contribution

It introduces and evaluates three distinct analysis methods, including a simple count summation and two Bayesian approaches, for estimating peak parameters in spectral data.

Findings

Method A is simple but limited to high signal-to-noise data.

Method B provides rigorous Bayesian estimates with reliable centroid uncertainties.

Method C offers accurate peak shape fitting with small uncertainties.

Abstract

The estimation of the signal location and intensity of a peak in a pulse height spectrum is important for x-ray and $\gamma$-ray spectroscopy, charged-particle spectrometry, liquid chromatography, and many other subfields. However, both the "centroid" and "signal intensity" of a peak in a pulse-height spectrum are ill-defined quantities and different methods of analysis will yield different numerical results. Here, we apply three methods of analysis. Method A is based on simple count summation and is likely the technique most frequently applied in practice. The analysis is straightforward and fast, and does not involve any statistical modeling. We find that it provides reliable results only for high signal-to-noise data, but has severe limitations in all other cases. Method B employs a Bayesian model to extract signal counts and centroid from the measured total and background counts. The resulting values are derived from the respective posteriors and, therefore, have a rigorous statistical meaning. The method makes no assumptions about the peak shape. It yields reliable and relatively small centroid uncertainties. However, it provides relatively large signal count uncertainties. Method C makes a strong assumption regarding the peak shape by fitting a Gaussian function to the data. The fit is based again on a Bayesian model. Although Method C requires careful consideration of the Gaussian width (usually given by the detector resolution) used in the fitting, it provides reliable values and relatively small uncertainties both for the signal counts and the centroid.