Possible Approach to Prediction of Harmonic Amplitudes in the Considered Signals
Citation
MLA Style: Alexey Alexeevich Lyubomudrov, Elman Said-Mokhmadovich Akhyadov, Yuriy Mikhailovich Lagusev "Possible Approach to Prediction of Harmonic Amplitudes in the Considered Signals" International Journal of Engineering Trends and Technology 69.3(2021):185-188.
APA Style:Alexey Alexeevich Lyubomudrov, Elman Said-Mokhmadovich Akhyadov, Yuriy Mikhailovich Lagusev. Possible Approach to Prediction of Harmonic Amplitudes in the Considered Signals International Journal of Engineering Trends and Technology, 69(3),185-188.
Abstract
This article describes the approach to the determination of harmonic amplitudes in the considered signals. The approach assumes multiplication of the considered signal containing harmonics by an auxiliary sinusoidal signal containing unit amplitude and harmonic frequencies of initial signal with the subsequent taking of definite integral of the generated product over time. This approach is validated by taking the exact integral of the initial signal presented by the sinusoidal constituent. It has followed from the exact solution that the integral value equals harmonic amplitude with the precision up to the coefficient and additive constituent. This has confirmed that the calculated integral is the amplitude-frequency spectrum. Then, for direct prediction of amplitude, the exact value of the integral without loss of correctness has been converted into the form suitable for parallel calculations using PC. The considered approach is valid, provided that the mutual influence of harmonics upon determination of amplitudes can be neglected.
Reference
[1] J. An, and D. Yang., Nonabelian harmonic analysis and functional equations on compact groups, Journal of Lie Theory, 21(2) (2011) 427–456.
[2] P. Bader, and S. Blanes., Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrodinger equations, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 83(4) (2011) 046711.
[3] I. Arregui, A. A. Ramos, and A. J. Diaz., Bayesian analysis of multiple harmonic oscillations in the solar corona, Astrophysical Journal Letters, 765(1) (2013) L23.
[4] Z. Avetisyan, and R. Verch., Explicit harmonic and spectral analysis in Bianchi I-VII-type cosmologies, Classical and Quantum Gravity, 30(15) (2013) 155006.
[5] J. Barros, and R. I. Diego., A discussion of new requirements for measurement of harmonic distortion in modern power supply systems, IEEE Transactions on Instrumentation and Measurement, 62(8) (2013) 2129–2139.
[6] A. K. Britenkov, and N. S. Stepanov., Analysis of acoustic and vibration signals with the help of generalized spectral-analytic method, Mechanical engineering and engineering education, 3 (2014) 20–31.
[7] Y. – S. Kim, D. – H. Kim, H. – Ch. Lee, and Ch. – W. Chung., Pulsed plasma measurement method using harmonic analysis, Journal of Applied Physics, 117(24) (2015) 243302.
[8] J. P. Kahane., Compressed sensing from a harmonic analysis point of view, Analysis Mathematica, 42(1) (2016)19–29.
[9] D. Beltran, and J. Bennett., Subdyadic square functions and applications to weighted harmonic analysis, Advances in Mathematics, 307(2017) 72–99.
[10] A. Ghaani Farashahi., Classical harmonic analysis over spaces of complex measures on cosset spaces of compact subgroups, Analysis Mathematica, 43(3)(2017) 461–473.
[11] A. A. Lyubomudrov., A Variant of Calculation of Harmonic Amplitude in Analyzed Signals Research, Journal of Pharmaceutical Biological and Chemical Sciences, 7(4)(2016) 1475–1480.
[12] A. A. Lyubomudrov., About the influence of the initial phase of the harmonic components on the current amplitude-frequency spectrum, Journal of Industrial Pollution Control, 33(1)(2017) 905–908.
[13] K. Drazil, J. Grajciar, T. Pavlicek, M. Celep, and M. Hudlicka., Harmonics effects on microwave power measurement using diode sensors, IEEE Transactions on Instrumentation and Measurement, 68(6)(2019) 1852–1859.
[14] A. A. Kharkevich., Spectra, and analysis, 5-th ed. Moscow, Russia: Publishing house "LIBROKOM", (2009) 112.
Keywords
spectral analysis, current amplitude-frequency spectrum, harmonics, amplitude, prediction of amplitudes.