Radiation detector signal processing using sampling kernels without bandlimiting constraints

For the development of digital signal processing systems for fast scintillation detectors we comprehensively study the modeling of nuclear signals, deconvolution of detector pulses and signal sampling. Applications for new scintillators with light decay times of a few nanoseconds demand suitable low power digital systems running at lowest possible sampling rates. We are interested in accurate sub-nanosecond timing and optimal energy resolution. The generalized non-bandlimiting sampling theorems allow filter structures with lower than Nyquist sampling rates for certain signals, where the classical sampling theorem fails. Recently it was shown that, by using a sampling rate greater or equal to the rate of innovation, it is possible to reconstruct certain restricted signals uniquely. The class of sampling kernels that can be used contains transfer functions with rational Fourier transforms. We introduce a physically realizable sampling scheme combined with a deconvolution timing filter algorithm for radiation detector signals. The novel architecture achieves sub-sampling rate timing accuracy together with optimal energy resolution and a high throughput for LaBr₃:Ce scintillation detector system.