Classification of digital non-linear filters by discrete convolutions 

Mikhail A. Shcherbakov, Doctor of engineering sciences, professor, head of the sub-department of automation and remote control, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mashcherbakov@yandex.ru 

681.5.015 

10.21685/2072-3059-2021-4-9 

Background. In the field of digital signal processing, there are many problems that can not be solved with traditional linear filtering methods. In particular, the use of linear filtering does not allow separating signal from the noise in the case when the spectra of the useful signal and interference overlap. The purpose of this work is to research a class of digital nonlinear filters that have significantly wider capabilities than linear filters. Materials and methods. To describe the process of nonlinear filtering, a discrete Volterra representation is used, which makes it possible to represent a digital nonlinear filter in the form of a set of nonlinear discrete convolutions characterized by kernels of different orders. This representation is a natural generalization of digital linear filtering to the non-linear case. To reduce the dimensionality of the kernels and simplify the analysis of the nonlinear filtering process, the reference regions of digital nonlinear filters are limited to slices in the time and frequency domains. Results and conclusions. The proposed approach allows one to describe the variety of digital nonlinear filters defined on the slices of kernels from a single point of view, and to classify them in the time and frequency domains. As examples of use, the problems of noise suppression in pulsed and narrow-band signals are considered, the solution of which is impossible using linear filtering methods. The proposed classification of digital nonlinear filters makes it possible to reasonably choose the structure and characteristics of a nonlinear filter for solving various problems of digital signal processing. 

digital signal processing, nonlinear filtering, polynomial filters, Volterra series, discrete nonlinear convolutions 

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