Investigation and optimization of the deconvolution method for PMT waveform reconstruction

Photomultiplier tubes (PMTs) are extensively employed as photosensors in neutrino and dark matter detection. The precise charge and timing information extracted from the PMT waveform plays a crucial role in energy and vertex reconstruction. In this study, we investigate the deconvolution algorithm utilized for PMT waveform reconstruction, while enhancing the timing separation ability for pile-up hits by redesigning filters based on the time-frequency uncertainty principle. This filter design sacrifices signal-to-noise ratio (SNR) to achieve narrower pulse widths. Furthermore, we optimize the selection of signal pulses in the case of low SNR based on Short-Time Fourier Transform (STFT). Monte Carlo data confirms that our optimization yields enhanced reconstruction performance: improving timing separation ability for pile-up hits from $7\sim10$~ns to $3\sim5$~ns, while controlling the residual nonlinearity of charge reconstruction to about 1\% in the range of 0 to 20 photoelectrons.