Optimal Linear Filters for Pulse Height Measurements in the Presence of Noise

摘要

For measurements of nuclear pulse height spectra a linear filter is used between the pulse amplifier and the pulse height recorder so as to improve the signal/noise ratio. The problem of finding the optimal filter is investigated with emphasis on technical reliability. The maximum available signal/noise ratio is theoretically calculated on the basis of all the information which can be found in the output of the pulse amplifier, and on an assumed a priori knowledge of the pulse time of arrival. It is then shown that the maximum available signal/noise ratio can be obtained with practical measurements without any a priori knowledge of pulse time of arrival, and a general description of the optimal linear filter is given. The solution is unique, technically realizable, and based solely on data (noise power spectrum and pulse shape) which can be measured at the output terminals of the pulse amplifier used.