Nuclear Instruments and Methods. October 1983

Real Time Spectrum Analysis
by Andy Blunden, D G O'Prey & W H Tait, April 1983.

A method is described for the separation of a composite pulse-height spectrum into its unresolved component parts, which belong to a set of measured library spectra. The method allows real-time estimation giving running estimates during acquisition of the spectrum, minimises computation space, especially for a number of parallel calculations, estimates in advance the rms errors, and produces a significance measure for the hypothesis that the composite contains only the library spectra.

Least squares curve-fitting, and other methods, can be compared, with the formalism developed allowing analytical comparison of the effect of detector energy resolution and detection efficiency. A rational basis for the choice between the various methods of spectrum analysis follows from the theory, minimising rms estimation errors. The method described is applicable for very low numbers of counts and poor resolution.

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This paper was written at the same time as I was reading Hegel's Science of Logic for the first time, and the structure of the paper reflects my understanding of the Logic at the time. The first part is a “genetic exposition”, posing the problem and solving it, and then demonstrating the fallacy in this solution leading to a new solution. I.e., according to the logic of Hegel’s Doctine of Essence. The second part then presents a Notion in the form of a new formalism and proves the thesis arrived at via the genetic distribution, mathematically, to be the best solution to the problem posed at the beginning. This leads then to a critique of Other methods of solution and a method of evaluating them, thus the Idea. This aspect of the paper is not made explicit and my collaborators at the time were not aware of it.