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Laser Doppler vibrometry is actively used in experimental studies because of its noncontact measurement technique. When using a stationary laser to measure the vibrations of rotating bodies and Fourier transform to process the results of such measurements, a problem arises, associated with a decrease in the frequency resolution of the spectra with increasing rotation rate of the body. As a result, at sufficiently high rotation rates, closely spaced discrete components may cease to be resolved. This paper proposes a method for solving such a problem using the least squares method. The operability of this processing method has been demonstrated on experimental data.