Low-Pass Filtering Method for Poisson Data Time Series

Victor Getmanov,Anna Dmitrieva,Vladislav Chinkin,Mikhail Dobrovolsky,Nataliya Osetrova,Roman Sidorov,Anna Kovylyaeva,Alexei Gvishiani,Anatoly Soloviev,Igor Yashin

doi:10.3390/app11104524

Abstract

Problems of digital processing of Poisson-distributed data time series from various counters of radiation particles, photons, slow neutrons etc. are relevant for experimental physics and measuring technology. A low-pass filtering method for normalized Poisson-distributed data time series is proposed. A digital quasi-Gaussian filter is designed, with a finite impulse response and non-negative weights. The quasi-Gaussian filter synthesis is implemented using the technology of stochastic global minimization and modification of the annealing simulation algorithm. The results of testing the filtering method and the quasi-Gaussian filter on model and experimental normalized Poisson data from the URAGAN muon hodoscope, that have confirmed their effectiveness, are presented.

Highlights

Poisson data time series from muon hodoscope (MH) according to (2), which begins from the values Y
For the dimension r0 = 8 and the assigned cutoff frequency wc = 0.1 we find out the final cutoff frequency wc f = 0.275; let us denote the frequency response (FR) as H f (w, wc f )
The proposed filtering method for time series of normalized Poisson-distributed data, which was based on the developed digital low-pass quasi-Gaussian filter with a finite impulse response, a gain equal to one at low frequencies and non-negative weighting coefficients, turned out to be efficient; the FR of the low-frequency quasi-Gaussian filter of small dimension was characterized by a better approximation to the prototype filter FR

Summary

Introduction

Academic Editors: Roberta Sparvoli and Matteo Martucci. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The article proposes a low-pass filtering method for Poisson-distributed data time series, based on a specially developed digital low-pass filter with finite impulse response (FIR filter), with gain equal to one at zero frequencies and non-negative weighting factors. Low-pass filtering is applied in order to reduce noise in Poisson-distributed data to ensure the recognition of emerging fluctuations of mathematical expectations in them. Poisson-distributed, or Poisson data are found in various physical systems, for example, related to the heliosphere and magnetosphere of the Earth; the fluctuations of mathematical expectations of these data may contain information regarding the structures and characteristics of these systems

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Discussion

Conclusion