Implementation of an Adaptive Trapezoidal Shaping Method Based on FFT

Trapezoidal shaping algorithms are often used when digitally processing spectrum detector signals to reduce the ballistic deficit, improve energy resolution, and increase the count rate. In the digital trapezoid shaping algorithm, adjusting the rise and flat-top times of the trapezoid is easy. The two stacked exponential pulses can be shaped into two peak-distinguishable trapezoids, allowing them to be preserved during pile-up rejection processing. The pulse signal output by the energy spectrum detector usually needs to be converted into a pulse that is near exponential decay through a charge-sensitive preamplifier. However, the effects of detector aging and temperature drift can always change the decay constant of the output signal, which may severely distort the shaped trapezoidal signal and reduce the energy resolution of the detector. In this article, based on the digital synthesis of pulse shapes, we propose using the fast Fourier transform (FFT) algorithm to calculate the decay constant of the exponential pulse. This method can adaptively evolve new shapers according to different detector characteristics and support a fast calibration procedure to match different noise spectra and address unpredictable signal fluctuations. The adaptive trapezoidal shaping system was implemented in the field-programmable gate array (FPGA), and the relative error of the coefficients obtained from the system was verified by simulation and experimentation to be within 0.8%.