Features of signal sampling and reconstruction in nonlinear systems

Abstract

Background. Digital signal processing involves sampling continuous signals. Unlike linear systems, performing this operation in nonlinear systems has a number of features associated with expanding the spectrum of the output signal. The purpose of this research is to study the sampling of signals in nonlinear systems when solving problems of modeling the dynamics of the system and restoring the output signal. Materials and methods. A class of nonlinear systems defined by the Volterra expansion is considered. Discrete nonlinear filters are used to digitally simulate system behavior. The spectral representation of nonlinear systems through multidimensional characteristics (kernels) in the frequency domain is used. Results and conclusions. The choice of sampling frequency in nonlinear systems is determined by the type of problem being solved. At the same time, the tasks of identifying the dynamic characteristics of the system and restoring the output signal of the system are highlighted. For the linear case, these problems are identical and their solution is achieved by choosing the sampling frequency of the input signal in accordance with Kotelnikov’s theorem. It is shown that the effect of expanding the spectrum of the output signal imposes different requirements on the choice of sampling frequency when solving problems of identifying and restoring the output signal in nonlinear systems.

Keywords

• digital signal processing
• nonlinear filtering
• signal sampling
• polynomial filters
• volterra series
• signal spectrum