MATRIX REALIZATION OF TWO-DIMENSIONAL DISCRETE VOLTERRA FILTERS

Shcherbakov Mikhail Aleksandrovich, Doctor of engineering sciences, professor, head of sub-department of automation and remote control, Penza State University (40 Krasnaya street, Penza, Russia), mashcherbakov@yandex.ru
Sazonov Vladimir Vasil'evich, Candidate of engineering sciences, associate professor, sub-department of automation and remote control, Penza State University (40 Krasnaya street, Penza, Russia), mashcherbakov@yandex.ru
Isyanov Ruslan Nikolaevich, Candidate of engineering sciences, associate professor, sub-department of automation and remote control, Penza State University (40 Krasnaya street, Penza, Russia), mashcherbakov@yandex.ru

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Background. The object of the research is multidimensional discrete Volterra fil-ters (VF, polynomial filters), determined by a section of a discrete functional series. The subject of the research is the methods of VF effective realization, based on representation thereof in matrix form and decomposition procedure perfomance. The article is aimed at development of ways of effective realization of two-dimensional discrete VF due to paralleling and unification of computing operations.
Materials and methods. To describe the process of multidimensional discrete filtration the authors used matrix representation of VF. The researchers introduced a notion of sectional convultion allowing to reduce calculation of matrix non-linear convultions to a sequence of calculations of regular two-dimensional convultions, and to estimate the volume of necessary calculations.
Results. The authors suggest an approach to realization of two-dimensional discrete VF, based on decomposition of matrix representation on non-linear two-dimensional convultions. The given approach allows to reduce the problem of non-linear VF realization to series-parallel execution of regular two-dimensional convul-tions and may serve as a foundation for development of parallel computational structures intedned for realization of high-speed algorithms of non-linear filtration through parallel process matrix application.
Conclusions. The method of realization of two-dimensional discrete VF, based on execution of decomposition of the matrix representation of non-linear convultions, allows to use the known methods and algorithms of multidimensional filtration for realization of VF and to give clear interpretation thereof. The suggested method of VF realization through using series-parallel execution of calculations provides an opportunity of realization thereof on the basis of application of structures of systolic processes.

digital signal and image processing, non-linear filtering, filters Volterra, polynomial filtering, parallel calculations.

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