Авіаційно-космічна техніка та технологія (Nov 2018)
FILTERING SIGNALS ON THE BASE OF CUMULANTS
Abstract
The subject of study is the integration of linear and nonlinear methods for the solution of image restoration applications. The aim is the development of signal filtering algorithm and image model building. The tasks are to develop a criterion for impulse form signals; to develop an effective solving algorithm. The applied methods are optimal filtering method, mathematical models of optimization, the method of independent component analysis. The results are the following: the problem of choosing the optimal structure of the algorithm is formulated, complexing of linear and nonlinear methods for solving the inverse problem is considered, the criterion of optimization for signals of the impulse form, the optimization criterion for pulse signals is selected. The criterion is applied to select the filter kernel. The results of control restorations for distorted images are presented. The recovery error is estimated as a function of the signal-to-noise ratio. Conclusions. The following new results are obtained: the method of optimal filtering based on a cumulant of the second order for pulsed signals has been improved by introducing an appropriate criterion. The obtained estimate is used to form a linear model of observation. The solution of the obtained system of linear equations (SLE) is found in the framework of the analysis of independent components (ICA), based on the fourth-order cumulant. A model of the distorted image is constructed and the results of the reconstruction are given. It is shown that for impulse waveforms, it is possible to apply the stopping criterion of the iterative process on the basis of higher-order derivatives. The quality of filtration in the norm of L2 is estimated depending on the signal-to-noise ratio. The simulation results show that the recovery error decreases at ratios more than 10. The results of the studies performed in this paper can be used in the development and modernization of various radio engineering systems of aircraft
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