Aspects on Harmonics Analytical Identification of a Periodic Non-Sinusoidal Wave

Multiple fields of science and social life use representations of time variations for physical, chemical, biological, statistical variables. When the representation of these variables versus time is periodic, the use of the discrete Fourier transform to identify harmonics and continuous components represents an immediate solution, favored by the affordability of data acquisition and computer assistance. Research over the past two decades has highlighted some major aspects in the field of harmonic composition identification of periodic non-sinusoidal waves, such as the alternative current “alias” phenomenon, the maximum harmonic order that can be determined by discrete Fourier transform, as well as the possibility of appearance of the direct current “alias” phenomenon, i.e. on the continuous component of the analyzed wave. This work has three objectives related to the analytical identification of a periodic non-sinusoidal wave harmonics. Firstly, it is determined a system of three equations, of which a transcendent one, based on which the three unknown parameters of a harmonic are calculated: the amplitude, the order and the phase. Initial data are represented by the coordinates of three different points. The second aspect approached is represented by the harmonic analysis of a periodic non-sinusoidal wave with a finite number of harmonics and highlighting the manifestation modalities of alias phenomena. Finally, the third objective deals with the use of an odd number of samples over a period, a case so far avoided due to a small simplification in writing the computational relationships, but which may occur frequently due to the frequency variations at the fundamental level (such as in power systems).