Analysis of spectra of multi-frequency phase-manipulated signals

A spectral analysis of multi-frequency radio signals generated by phase modulation of a high-frequency harmonic oscillation by a phase-manipulated intermediate-frequency signal was performed. Based on the obtained expression for the spectrum of the complex contour of the multi-frequency phase-manipulated signal at the output of the phase modulator, the components of its spectrum were analyzed depending on the modulation parameters. It was established that the amplitude of the components of the spectrum and their number in the spectrum are determined by the parameters of the Bessel function of the first kind of the real argument – the phase modulation index. The value of the phase modulation index depends on the amplitude of the modulating phase-manipulated intermediate frequency signal and the steepness of the phase modulation characteristic of the modulator. The frequency difference between adjacent components of the multi-frequency spectrum is uniquely determined by the intermediate frequency of the modulating phase-manipulated signal. The spectral components of the multi-frequency spectrum are periodic functions of sinc(x) spectra and spectra of phase-manipulated signals, and the width of these spectra is determined by the duration of the modulating phase-manipulated signal and the duration of the discrete time, respectively. According to the nature of the change of the spectrum parameters from the modulation parameters, the multi-frequency phase-manipulated signal can be classified as a complex broadband signal. Formation of multi-frequency phase-manipulated signals is carried out by single-channel devices. The practical application of the studied signals provides an opportunity to potentially increase the energy and structural stealth of radio communication systems, implement adaptation modes in radar systems, and determine the multiplicity of phase manipulation of phase-manipulated signals of telecommunication systems when organizing technical information protection.