Analysis of the Harmonic Components of Signal Based on the Values Measured at Nonequidistant Mesh Points of an Equidistant Mesh with a Finite Length That Is Equal to the Number of Residues Modulo a Prime

摘要

A method for nonequidistant measurements of signals on an equidistant mesh with a finite length equal to the number of residues modulo a prime p_1 is proposed to determine parameters of the harmonic components of signal. The measurements are performed at the mesh points with the numbers that correspond to the primitive roots modulo a prime p_1, which provides a decrease in the number of measurements and an increase in the radar capacity by a factor of 2-5. At a given number of nonequidistant measurements on the equidistant mesh with a relatively large number of mesh points, an interval of the unambiguous measurements of the longitudinal size (based on the multifrequency signal) or Doppier frequency (based on a train of single-frequency pulses) can be increased. It is demonstrated that the spectrum of signal constructed with the aid of such measurements reproduces spectral lines of harmonic oscillations contained in the signal for both coherent and incoherent signal processing. A procedure for the reconstruction of the signal at the missing equidistant mesh points using the interpolation Legendre polynomials based on the nonequidistant measurements is proposed. A further weighted processing of the reconstructed signal and the formation of spectrum using the Fourier transform will provide a decrease in the level of side lobes.