A method for mathematically synthesizing double-exponential signal generation on-the-fly on FPGA and its evaluation

This paper introduces a high-precision, FPGA-based analog signal generator that fundamentally departs from conventional, template-based approaches by mathematically synthesizing each analog pulse in real time. Unlike systems relying on pre-recorded or pre-defined waveform memories, the proposed architecture dynamically computes every sample of double-exponential pulses on-the-fly within reconfigurable FPGA logic. Leveraging the AMD Xilinx ZYNQ 7010 SoC, the system ensures that every pulse is uniquely tailored on demand, with full control over rise time, decay time, amplitude, and pile-up effects. This real-time, parameter-driven signal generation enables the accurate emulation of complex detector signals, including overlapping events and user-defined spectral distributions, while guaranteeing deterministic timing and minimal processor overhead. Experimental results demonstrate that the platform can precisely reproduce the analog characteristics and statistical features of diverse scintillation detector responses, outperforming commercial solutions limited to simple exponential or static waveform outputs. The modular, runtime-reconfigurable design supports dual-channel, high-fidelity operation and can be extended to broader application domains, including medical signal emulation and telecommunication waveform synthesis. By eliminating dependence on static pulse templates, this work establishes a new standard for flexibility, realism, and accuracy in embedded hardware testing and detector development.