The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach

• Published in: Inventions (Basel) 2020-06, Vol.5 (2), p.15
• Main Authors: Sokolov, Sergey, Marshakov, Daniil, Novikov, Arthur
• Format: Article
• Language: English
• Subjects: current time interval; differential equations; generalized differentiation; Runge–Kutta method; spectrum generation algorithm; spectrum of non-periodic functions
• ISSN: 2411-5134; 2411-5134
• DOI: 10.3390/inventions5020015

The paper deals with the problem of forming spectra of non-periodic signals in real-time. The disadvantage of the existing approaches is the dependence of the formed spectrum on time as a parameter and the possibility of obtaining the signal spectrum in its original definition only for a fixed time, as well as a high amount of computation. In this regard, a computationally efficient algorithm is proposed for forming a spectrum of non-periodic functions on a time interval that is constantly updated with a given sampling step, which ensures the invariance of the generated spectrum to time as a parameter. The algorithm is based on obtaining differential equations that are based on generalized differentiation with respect to a variable time interval of spectral components and their solving while using the fourth-order Runge–Kutta method. A numerical simulation of the developed algorithm was performed using the MATLAB mathematical modeling package using the example of a substantially non-linear function. Based on the practical results, a comparative evaluation of computational and time complexity has been performed in solving the problem. Based on the obtained experimental results, it is concluded that it is possible to effectively use the proposed algorithm to calculate the current spectrum of non-periodic functions with the requirement of small sampling steps, i.e., when calculating the spectrum in real-time.