Observations of the daily 1- to 8-Å solar X-ray emission from 1977 to 1981 are analyzed from a terrestrial viewpoint. A high-resolution method of anharmonic frequency analysis is used to search for discrete frequencies in a finite time series and estimate the frequency, phase, and amplitude of each periodic component. The time series data are the broadband, full disk X-ray measurements, primarily from the GOES 2 satellite, and are reduced from 3-s data to a daily nonflare index representing background coronal emission. Intermediate-term epochs are weakly stationary time intervals about 128 days long and correspond to major intervals of solar activity over about four and a half rotations. Time series of background X-ray flux longer than about 128 days are nonstationary. Results suggest that near the boundary of an epoch the amplitude specctrum undergoes an episodic change in frequency, phase, and amplitude, after which a new spectrum appears that persists for the duration of the next epoch. Furthermore, those frequencies most closely corresponnding to solar rotation are not normally distributed about a 27-28 day mean but ocur at about 22, 25, and 34 days.