Periodic functions with variable period – basic concepts and certain investigation results

Abstract

Investigation of real signals is one of the most important applied areas of mathematics. According to their properties, signals are quite diverse, and methods of their research are different as well. Among this diversity, periodic signals with variable period make up a significant proportion. Till present, no attention was paid to the theory of such signals. In this paper, we define periodic functions with variable period, which are the model of these signals. Some properties of the variable period are considered. Examples of the analytical formulation of functions with variable period in the form of trigonometric functions with variable period are given and their variable periods are recorded. It is pointed out that these functions can be used as basic ones for constructing orthogonal system of trigonometric functions with variable period and its use for constructing Fourier series of functions with variable period.