Signal Change Estimation of One Important Class in the Filtering Process

Abstract

This paper considers the problem of the measure of the signal change from the Weyl-Nagy class of differentiable functions when the signal is filtered by means of weight functions. Asymptotic estimates characterizing the measure of the signal change of the specified class of Weyl-Nagy differentiable functions have been established. The difference in signal filtering described by both differentiable and non-differentiable functions has been shown. The established signal change estimates have been demonstrated by applying a specific low-pass filter to the given signal. This example illustrates the difference between differentiable and non-differentiable signal filtering. The behavior of the measure of signal change depending on the filter parameters and the maximum order of the derivative function characterizing the signal has been also shown.