  A digital shaper for high-count-rate detection and amplitude measurement of
pulses is proposed and analysed in this paper. The proposed shaper converts
pulses with a short leading edge and a long exponential tail into a true
Gaussian form. The width of Gaussian pulses can be several times smaller than
the rise time of the input pulses, i.e. considerably shorter than the
undistorted output pulses provided by standard shapers. Therefore, the proposed
true Gaussian shaper resolves strongly overlapped pulses better and provides a
higher output count rate. The capabilities of the proposed true Gaussian shaper
are analysed with real and simulated output signals of a silicon drift detector
of soft X-ray radiation, operating at a high count rate of the collected
quanta. Our analysis shows that true Gaussian shapers can increase the count
rate of spectrometer systems several times compared with the widely used
trapezoidal shapers, while maintaining their amplitude resolution.
