Probability Density Function Transformation Using Seeded Localized Averaging
Dimitrov, Nedialko B.
Jordanov, Valentin T.
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Seeded Localized Averaging (SLA) is a spectrum acquisition method that averages pulse-heights in dynamic windows. SLA sharpens peaks in the acquired spectra. This work investigates the transformation of the original probability density function (PDF) in the process of applying the SLA procedure. We derive an analytical expression for the resulting probability density function after an application of SLA. In addition, we prove the following properties: 1) for symmetric distributions, SLA preserves both the mean and symmetry. 2) for unimodal symmetric distributions, SLA reduces variance, sharpening the distributions peak. Our results are the first to prove these properties, reinforcing past experimental observations. Specifically, our results imply that in the typical case of a spectral peak with Gaussian PDF the full width at half maximum (FWHM) of the transformed peak becomes narrower even with averaging of only two pulse-heights. While the Gaussian shape is no longer preserved, our results include an analytical expression for the resulting distribution. Examples of the transformation of other PDFs are presented.
IEEE Transactions on Nuclear Science, January 2012The article of record as published may be located at http://dx.doi.org/10.1109/TNS.2011.2177861
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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