Abstract
The article considers the harmonic analysis of periodic non-sinusoidal oscillations by Fourier series expansion. The features of decomposition of even and odd functions are revealed. Based on the symbolic method, the Fourier series was presented in a complex form. Examples are presented to provide clarity of the steps of the procedures for decomposing a function into a Fourier series. Examples of Fourier series decomposition of periodic non-sinusoidal electric currents or signals using the Mathcad application software package are considered. Graphical, numerical, and analytical solutions of non-sinusoidal periodic currents or signals have been obtained using computational experiments. Methods for calculating the sum of the terms of the Fourier series for non-sinusoidal periodic signals, which consist of several stages, are presented. It has been proven that complex even and odd functions describing periodic currents that are not sinusoidal (or cosine-shaped) consist of the sum of simple harmonic electrical oscillations. These fluctuations make up the frequency spectrum of these currents. The results of the approximation of periodic signals are presented as a Fourier series over the interval (p, p). Electrical signals are classified into a Fourier series, and the sum of the first two and four terms of this series is obtained. It has been shown that the more members of the signals classified in a row, these members more accurately describe the signal under study.