Gaussian pulses have good time and frequency domain characteristics, and perform well in terms of signal-to-noise ratio, ballistic loss, and other aspects of the synthesis. When performing Gaussian pulse shaping, errors introduced by hardware limitations may lead to differences in shaping results. Compared to infinite impulse response (IIR) filters, finite impulse response (FIR) filters have the advantage of being less affected by errors and more stable.

This study aims to propose a FIR filter-based Gaussian pulse shaping algorithm using impulse response functions, and realize a FPGA-based hardware implementation of this algorithm to evaluate the impact of hardware limitations on it.

First of all, the discrete impulse response of Gaussian pulse shaping (GPS) was derived by means of impulse response invariant transformation, and shaped pulse waveforms under different quantization accuracies and truncation intervals were obtained using a computer simulation, so did that under Gaussian pulse shaping with or without additional truncation were assessed. Then, X-ray fluorescence signals emitted by Mn sample was acquired using fast silicon drift detector (FAST-SDD) to assess shaping performance on the spectrum, and processed by a digital multichannel analyzer utilizing FIR GPS algorithm implemented in a field programmable gate array (FPGA) processing board. Finally, peak area and energy resolution of the spectrum were used to compare performances of GPS under different quantization accuracies and truncation intervals, as well as performances of three methods of trapezoidal pulse shaping, Gaussian pulse shaping with additional truncation method and normal GPS.

For comparisons of quantization accuracy, when the quantization accuracy is greater than 4 bits, the shaping performance of GPS remains consistently stable within the peaking time ranging from 120 ns to 1 140 ns when the quantization accuracy is greater than 4 bits. Otherwise, the influence of low quantization accuracy on GPS is minimized ranging from 420 ns to 780 ns. For inter-method comparisons, GPS with or without additional truncation outperform trapezoidal pulse shaping. The truncated GPS algorithm has better energy resolution and saves more hardware resources, whilest the normal GPS algorithm owns better pulse pile-up rejection capability for the same peaking time.