Development of a novel approach for precise pulse height extraction using Lagrange interpolation

Pulse height measurement is one of the most important step in ionizing radiation spectroscopy. However, the conventional analog and digital peak detection methods may be limited due to their high complexity and cost. In this work, a simple and novel mathematical approach based on Lagrange interpolation has been developed to precisely extract pulse height from a sequence of samples recorded at a low rate (2 MS/s). This has been implemented in an ARM-based micro-controller to construct a full functionality multi-channel analyzer. The results showed that the multi-channel analyzer has a very good integral linearity response (<0.1 %) and reasonable full width at half maximum (3.4 channels) over the entire analog-to- digital converter range. The pulse height spectrum, which was recorded using an HPGe detector, demonstrated high performance of multi-channel analyzer in the spectroscopy experiments, leading to a resolution of about 0.2 % at 1332.5 keV.