Analysis of Structural Differences of Signals Formed in the Basis of Fourier and Wavelet Functions

Abstract

The results of the study are proposed, showing the theoretical substantiation of the possibility of using wavelets for the synthesis of signal structures based on them. Considering that wavelets are localized in both frequency and time space, it is proposed to synthesize phase-shift keyed signals on their basis. It is shown that the conditions that determine the legality of their application for the transmission of discrete information are valid for wavelets. Signal constructions of phase shift keying, analogous to signals of double phase shift keying, are substantiated on the basis of wavelets. A structural model has been developed for the synthesis of BPSK signal structures both based on harmonic Fourier functions and based on wavelets. The stages of synthesis are described in detail. The results of the study of structural differences in signal structures formed in the basis of wavelets and Fourier functions are presented. The values of peak factors and functional changes in the energy level on the duration of the symbol for the wavelet and sinusoid are calculated. The time intervals are substantiated within which 95% of the signal energy is localized. The function of the difference in energy growth is presented, which made it possible to determine the boundaries of the passband of the filters when compensating for the aiming noise in the spectrum. It is shown that narrowing the optimal bandwidth of the receiving path by a factor of 2.29 will lead to a loss in energy for the wavelet by only 19%, while the loss in the sinusoid will reach more than 62%. It is shown how the structural differences between wavelets and sinusoids will be reflected in the behavior of the formed difference functions. An estimate of the noise immunity for wavelet signals compared to BPSK signals is presented.