The problem of processing correction of signals observed against the background of noise has been considered in relation to their spectral analysis by the Root-MUSIC method using the technology of surrogate autocovariance functions (ACF) of observation. The results of simulation modeling are presented dealing with the correction of observation processing by means of the phase randomization of spectral components of observation ACF using the ATS-algorithm for generating the observation surrogate ACF. It has been shown that in generating surrogate data from the observation ACF, ATS-algorithm ensures the highest efficiency at small signal-to-noise ratios.