Background. Currently, the main method to obtain information about the harmonic composition of a signal is to decompose the signal into a Fourier series. This decomposition brings to a convolution of the signal from the domain of instantaneous values into the domain of amplitudes and phases of harmonics of the original signal. However, in a number of vector calculation problems, such signal convolution is an undesirable phenomenon, since further operations are carried out in the domain of instantaneous values of the corresponding harmonics. Application of the properties of trigonometric functions makes it possible to develop a method to convert instantaneous signal values into instantaneous harmonic values with varying degrees of harmonic separation in the received signals and varying operation times.
Materials and methods. Analytical and numerical methods to solve linear equations have been used to solve the problems posed in this study. Analytical methods are presented by the obtained expressions to decompose the signal into harmonic series. Numerical methods have been used to test the filtering methods proposed in the study and have been implemented using the Python programming language.
Results. The author has proposed the methods to convert a signal into a series of instantaneous harmonic values using trigonometric principles. These methods have been tested on a mathematically modeled signal. Reliable results have been obtained, comparable to the results of a similar algorithm.
Conclusions. The proposed methods have variability and flexibility when choosing the time spent on filtering and the accuracy of the obtained result. A comparison with the Fourier transform has shown similar results in the presence of harmonics and noise, and better results in the presence of an aperiodic component.