Recursive Algorithms for Real-Time Digital ${\rm CR}!-!({\rm RC})^{\rm n}$ Pulse Shaping

This paper reports on recursive algorithms for real-time implementation of CR-(RC)ⁿ filters in digital nuclear spectroscopy systems. The algorithms are derived by calculating the Z-transfer function of the filters for filter orders up to n=4 . The performances of the filters are compared with the performance of the conventional digital trapezoidal filter using a noise generator which separately generates pure series, 1/f and parallel noise. The results of our study enable one to select the optimum digital filter for different noise and rate conditions.