Implementation of a truncated cusp filter for real-time digital pulse processing in nuclear spectrometry

In this work the transfer function for a truncated cusp infinite impulse response (IIR) filter has been derived. The truncated cusp filter, when given an exponential pulse in the presence of white noise, outputs a truncated cusp pulse which is optimum pulse shape under the constraint of finite pulse duration. However it features a pole outside of the unit-circle and is therefore inherently unstable. To overcome this instability a switching algorithm with two alternating poles has been applied. The filter has been simulated with MATLAB and Simulink and implemented on-board a FPGA. The pulses from a waveform generator and silicon drift detector (SDD) have been also processed by the filter and results compared with theory. We find that the simulation and measurements were in agreement and show that energy resolution due to electronic noise can be improved by up to 7.5% using a truncated cusp instead of triangular filter. An improvement of up to 2.8% in overall energy resolution was measured with a typical X-ray spectrometer based on a SDD detector with a nominal energy resolution of 150 eV at energies of MnKα line.