Use of Transformations in Multiparameter Data Sorting

A major problem in multiparameter data sorting is the excessive computer memory space required for all of the available information. This paper describes a sorting technique which is useful if the information in one parameter can be represented by a simple distribution which can be described by the coefficients of an appropriate transformation. It is possible to compute the coefficients without accumulating the data in spectral form. For example, consider a three parameter experiment where the events are characterized by x, y and f(x,y). Suppose that the purpose of the experiment is to map the amplitude, mean, standard deviation, skew and kurtosis of f(x,y) over the x-y plane. It is necessary to reserve only five words in the computer memory for each location in the x-y plane. During the sorting process, the quantities accumulated in these five registers are ΣΣ0i, Σa1i, Σa2i, Σa3i, Σa4i, where ai is the digital value of f(x,y) for the ith event. Use of the Gauss-Hermite quadrature and the Fourier transformation are discussed and illustrated by an example (the measurement of secondary electron yields as a function of fission fragment mass and energy).