# Low-Pass Filtering Method for Poisson Data Time Series
## 5 Conclusions  
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 than the FR of common FIR filters.  
Testing the filtering method based on the quasi-Gaussian filter for the problems of recognizing small in duration and magnitude fluctuation decreases (increases) in mathematical expectations using statistical modeling and statistical tests have confirmed its effectiveness:  
* The proposed method provided a decrease in errors in the filtered time series in comparison with the error values for standard FIR filters, by \(\approx\)15-30%; the method made it possible to recognize the mathematical expectation fluctuations with a relative decrease of 0.02 and duration of \(\approx\)12-24 h;
* The proposed method and the developed quasi-Gaussian filter provided relative error coefficients for mathematical expectation and root mean square values that appeared to be \(\approx\)10-30% less than the error coefficients for common FIR filters.  
Testing the method and the low-frequency quasi-Gaussian filter on experimental Poisson data made it possible to draw a conclusion about its satisfactory capabilities for recognizing decreases with relative decrease coefficients \(\approx\)0.020-0.030.  
The proposed method of noise reduction and a quasi-Gaussian filter have favorable prospects of using radiation particle counters for digital information processing in problems of experimental physics and measuring technology.  
Conceptualization, V.G., A.S. and I.Y.; methodology, V.G.; software, V.G. and V.C.; validation, M.D., A.G. and A.S.; formal analysis, V.C.; investigation, A.S.; resources, A.G.; data curation, A.D., A.K. and N.O.; writing--original draft preparation, V.G.; writing--review and editing, R.S. and M.D.; visualization, V.G.; supervision, I.Y.; project administration, A.S.; funding acquisition, A.G. All authors have read and agreed to the published version of the manuscript. This work was funded by the Russian Science Foundation (project No. 17-17-01215). Data Availability Statement: Data sharing is not applicable to this article. The results of experiments presented in this research rely on data collected by the Scientific & Educational Centre NEVOD, National Research Nuclear University MEPhI. We acknowledge URAGAN muon hodoscope data provided by the NEVOD institution. This work employed facilities and data provided by the Shared Research Facility \"Analytical Geomagnetic Data Center\" of the Geophysical Center of RAS ([[http://ckp.gcras.ru/](http://ckp.gcras.ru/)]([http://ckp.gcras.ru/](http://ckp.gcras.ru/))) (accessed on 19 April 2021). We would like to thank two anonymous reviewers whose valuable comments helped to improve the manuscript and properly demonstrate the results of our research. The authors declare no conflict of interest.