Cosine function shaping (or cos shaping) is used to digitally shape nuclear pulse signals, as the shaping method is simple and has high operability and flexibility.

This study aims to explore different cosine shaping methods of nuclear pulse signals, and evaluate their effect.

Firstly, based on the single exponential decay signal and cosine pulse signal, transfer functions and cascade formulas of three different cosine shaping methods in the Z-domain were derived. The influence of the parameter selection on the shaping effect in the cosine shaping algorithm was analyzed. Then, the cosine shaping methods were developed for the simulated nuclear signals and the actual sampled nuclear signals, and the cosine shaping, amplitude extraction, and energy spectrum construction of the digital nuclear signals were implemented in the field programmable gate array (FPGA) system. Finally, the gamma (γ) energy spectrum of ¹³⁷Cs (NaI(Tl) detector) was evaluated using the different cosine shaping methods.

The results of γ energy spectrum from ¹³⁷Cs (NaI(Tl) detector) demonstrate the satisfactory performance of all three digital cosine shaping algorithms in terms of energy resolution and counting. The symmetric zero-area cosine shaping performance index is improved relative to conventional methods.

The three kinds of digital cosine shaping methods all achieve accurate cosine shaping for simulated and real nuclear signals. The three cosine shaping methods proposed in this study may be applied to shape functions in other research areas.