Field programmable gate arrays (FPGAs) are attractive for a digital spectrometer due to its advantages of digital signal processing. However, how to improve the versatility of the spectrometer and increase the operating frequency of the digital shaper has gradually become a limitation that needs to be resolved in the FPGA-based spectrometer. A solution to improve the universality of the FPGA-based digital spectroscopy system is presented in this work, and the implementation of the real-time digital signal processing unit is improved to obtain a higher operating frequency, and then the optimal parameters of the digital trapezoidal shaper and the processing unit are also discussed through a series of experiments; finally, a FPGA-based digital spectrometer is developed. With the HPGe detector, the spectrometer achieves excellent energy resolution performance of 0.35% at 662 keV, 0.25% at 1173.2 keV, and 0.23% at 1332.5 keV.