This is an analysis of certain aspects of using the CLEAN algorithm for Fourier analysis of short segments of time series and of time series consisting of short segments of length Delta T separated by very long irregular gaps. It is assumed that the time series contain a harmonic component of amplitude A with a period longer than the length of the longest of the segments of the time series plus white noise with dispersion N-2. Reliability plots are constructed for determining the ranges of the parameters (nu, phi) for which the CLEAN procedure can be used to determine the values of nu, the frequency, and phi, the phase of the harmonic component, with a given accuracy. The results of this analysis are used to search for harmonic components in the variation of the H beta line profile in spectra of the triple star delta Ori A obtained in 2004 with the BTA telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences.