Formation of Spectrally Efficient Signals Based on Wavelets
Александр Федотович Крячко, Sergey Viktorovich Dvornikov, Sergey S. Dvornikov · 2021 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF) · 2021
The article discusses an original approach that allows the formation of signals based on wavelets by digital synthesis. Its essence lies in the fact that they take the original wavelet and reset its time counts, which have a small amplitude. Then form a spectral representation of the truncated structure and zero the spectral coefficients with a small amplitude. These procedures are repeated until no beats in the spectrum are excluded. Implementation of this approach allows one to obtain signals with new physical properties. In addition, the possibility of synthesizing signals from wavelet fragments has been investigated. It is substantiated that the signal structures obtained on the basis of wavelets have a higher noise immunity, which is achieved by increasing the occupied frequency band. The analysis of the general properties of wavelets is carried out, including the possibility of reconstruction in the time domain from their spectra. The parameters of wavelets that can be modulated by information messages are considered. It is substantiated that the operation of scaling wavelets can be considered as an analog of the frequency for harmonic oscillations. It is shown how it is possible to synthesize manipulated signals with given frequency properties from wavelet fragments. It is shown that when the time periods of the existence of a sinusoid and a wavelet are equal, the spectrum of the latter occupies a much wider band. The results of the analysis of the energy distribution of the spectrum of the sinusoid and wavelet over the duration of their period are presented. An interesting point is considered, when the 15% of the time interval for a wavelet has an energy gain of only 0.7%, while for a harmonic pulse under the same conditions, the gain will be 10%. This fact served as the basis for digital synthesis of wavelets with new properties. The synthesis itself is defined in three stages. First, the initial wavelet is formed in the time domain and the time interval is set, within which no less than 99.3% of its energy is concentrated. Then the amplitude values are zeroed outside the allocated interval. After that, by means of Fourier transform, a frequency representation of a new design is formed, in which all spectral coefficients located outside the main lobe are also zeroed, thus ensuring the smoothness of the function. And at the last stage, the modified structure is again transferred to the time domain.