Open Access Open Access  Restricted Access Subscription Access
Simulated signal and the result of its filtering based on lower envelope

Intensity estimation of noise-like signal in presence of uncorrelated pulse interferences

Andriy B. Lozynskyy, Igor M. Romanyshyn, Bohdan P. Rusyn


The effective filtering of noisy signals is one of the topical and open problems of the processing of noisy signals characterized by the presence of pulse interferences. A robust approach to intensity estimation of noise-like signal in the presence of additive uncorrelated pulse interferences has been proposed. The presence of additive uncorrelated pulse interferences leads to an increase of dispersion of registered signal at separate sections with pulse interferences. The robustness of intensity estimation is achieved by reducing the influence of sections with pulse interferences. A variety of nonlinear filtering methods has been developed that are based on detecting the intensity using lower envelope: two-parameter recursive filter, dilation, limiting the derivative and order statistics. The numerical simulation was used to perform their comparison with the known most common methods. The numerical simulation confirmed the efficiency of the approach proposed for estimating the intensity of noise-like signal in the presence of additive uncorrelated pulse interferences. The developed techniques can be applied for signal processing in means of communications, measurement instrumentation, radio astronomy, and also for image processing.


noise-like signal; additive uncorrelated pulse interference; estimation of random signal parameters; robust method; nonlinear filtering

Full Text:



CHAKRABARTY, A. “Large deviations for truncated heavy-tailed random variables: a boundary case,” Indian J. Pure Appl. Math., v.48, n.4, p.671, 2017. DOI:

NAYAR, V.; KAMPOURIS, I.; SIVITOS, S. “Outliers: The dangers of not being one of the pack,” J. Investing, v.26, n.4, p.165, 2017. DOI:

KIM, J.; LEE, S. “A convenient approach for penalty parameter selection in robust lasso regression,” Commun. Statistical Applications Methods, v.24, n.6, p.651, 2017. DOI:

ATKINSON, A.C.; CORBELLINI, A.; RIANI, M. “Robust Bayesian regression with the forward search: theory and data analysis,” TEST, v.26, n.4, p.869, 2017. DOI:

DUQUE-PINTOR, F.J.; FERNANDEZ-GOMEZ, M.J.; TRONCOSO, A.; MARTINEZ-ALVAREZ, F. “A new methodology based on imbalanced classification for predicting outliers in electricity demand time series,” Energies, v.9, n.9, p.752, 2016. DOI:

GORYAINOV, V.B.; GORYAINOVA, E.R. “The influence of anomalous observations on the least squares estimate of the parameter of the autoregressive equation with random coefficient,” Vestnik MGTU im. Baumana. Ser. Natural Sci., n.2, p.16, 2016. DOI:

SHEVLYAKOV, G.; LYUBOMISHCHENKO, N.; SMIRNOV, P.A. “A few remarks on robust estimation of power spectra,” Austrian J. Statistics, v.43, n.4, p.237, 2014. DOI:

KOSAREVYCH, R.J.; RUSYN, B.P.; KORNIY, V.V.; KEROD, T.I. “Image segmentation based on the evaluation of the tendency of image elements to form clusters with the help of point field characteristics,” Cybernetics Systems Analysis, v.51, n.5, p.704, 2015. DOI:

RUSYN, B.; LUTSYK, O.; LYSAK, Y.; LUKENYUK, A.; POHRELIUK, L. “Lossless image compression in the remote sensing applications,” Proc. of 2016 IEEE First Int. Conf. on Data Stream Mining & Processing, DSMP, 23-27 Aug. 2016, Lviv, Ukraine. IEEE, 2016, p.195-198. DOI:

PALIY, I.; SACHENKO, A.; KURYLYAK, Y.; BOUMBAROV, O.; SOKOLOV, S. “Combined approach to face detection for biometric identification systems,” Proc. of 5th IEEE Int. Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, 21-23 Sept. 2009, Rende, Italy. IEEE, 2009, p.434-439. DOI:

FISHER, R.A. “On the mathematical foundations of theoretical statistics,” Phil. Trans. R. Soc. A, v.222, p.594, 1922. DOI:

BICKEL, P.J.; LEHMANN, E.L. “Descriptive statistics for nonparametric models. III. Dispersion,” The Annals Statistics, v.4, n.6, p.1139, 1976. URI:

STIGLER, S.M. “The changing history of robustness,” The Am. Statistician, v.64, n.4, p.277, 2010. DOI:

ATKINSON, A.; RIANI, M. “Introduction to Robust Statistics,” Proc. of 8th Int. Conf. of the ERCIM WG on Computational and Methodological Statistics, 12-14 Dec. 2015, Senate House, UK. 2015. URI:

NEYKOV, N.M. “Robust statistical modelling through trimming,” PhD Dissertation. Sofia, 2016.

KOLLER, M.; MACHLER, M. “Definitions of y-functions available in robustbase,” The Comprehensive R Archive Network, 2017. URI:

CROUX, C.; DEHON, C. “Robust estimation of location and scale,” in EL-SHAARAWI, A.H.; PIEGORSCH, W.W. (eds.). Encyclopedia of Environmetrics. John Wiley & Sons Ltd, Chichester, UK, 2013.

LEYS, Christophe; LEY, Christophe; KLEIN, Olivier; BERNARD, Philippe; LICATAA, Laurent. “Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median,” J. Experimental Social Psychology, v.49, n.4, p.764, 2013. DOI:

TYLER, D.E. “A short course on robust statistics,” The State University of New Jersey. URI:

GANDHI, M.A.; MILI, L. “Robust Kalman filter based on a generalized maximum-likelihood-type estimator,” IEEE Trans. Signal Processing, v.58, n.5, p.2509, 2010. DOI:

LEKHOVYTSKIY, D.I. “Adaptive lattice filters for systems of space-time processing of non-stationary Gaussian processes,” Radioelectron. Commun. Syst., v.61, n.11, p.477, 2018. DOI:

PRODEUS, A.M.; DIDKOVSKYI, V.S. “Objective estimation of the quality of radical noise suppression algorithms,” Radioelectron. Commun. Syst., v.59, n.11, p.502, 2016. DOI:

YANG, Y. “A signal theoretic approach for envelope analysis of real-valued signals,” IEEE Access, v.5, p.5623, 2017. DOI:

“Time series forecasting using exponential smoothing,” 2011. URI:

SERRA, J.; VINCENT, L. “An overview of morphological filtering,” Circuits Systems Signal Process., v.11, n.1, p.47, 1992. DOI:

AIVAZYAN, C.A.; ENYUKOV, L.D.; MESHALKIN, L.D. Applied Statistics: Simulation Principles and Data Preprocessing [in Russian]. Moscow: Finansy i Statistika, 1983.

© Radioelectronics and Communications Systems, 2004–2019
When you copy an active link to the material is required
ISSN 1934-8061 (Online), ISSN 0735-2727 (Print)
tel./fax +38044 204-82-31, 204-90-41