Distribution Function for Output of Certain Linear Filters for Random Input Events†
B Soucek · Journal of Electronics and Control · 1964
Statistical properties of the response of a linear filter to discrete stationary time series are analysed. The input time series consist of discrete random events having a known amplitude distribution. The analysis is carried out for a number of response functions of linear filters especially of interest in pulse.height spectrometry and in pulse signal detection The probability density function of the output stochastic process is calculated and plotted as a function of both the response function parameters, and the average rate and amplitude distribution of the input events. Attention is paid to the moan value, the standard deviation and the factors of skowness and excess of the output process. The normalized form of the calculated curves suitable for direct application on amplitude sensitive systems excited by random events is given. The theoretical results are confirmed by the experiments.