Properties of Low-Frequency Filters of One-Dimensional Signals with Limited Energy Spectrum

In this paper, the properties of low-pass filters of signals with limited energy that are important for digital signal processing have been investigated. In particular, some conditions for the adequacy of signal smoothing have been established. The properties formulated in the work have been strictly justified for the case of using Fourier series of signals from the considered class. These properties have been generalized to the Fourier transformation of a signal and their implementation has been demonstrated for a number of specific examples. Other examples of functions that have the properties introduced in the work have been also given. Further research has revealed the universality of the functions for which the properties established in the work are fulfilled. In particular, the possibilities of their application in solving other problems of digital signal processing have been given.