The interpretation of Fourier spectra in the time domain is critically examined. Power density spectra defined and calculated in the time domain are compared with Fourier spectra in the frequency domain for three different types of variability: periodic signals, Markov processes and random shots. The power density spectra for a sample of neutron stars and black hole binaries are analyzed in both the time and the frequency domains. For broadband noise, the two kinds of power spectrum in accreting neutron stars are usually consistent with each other, but the time domain power spectra for black hole candidates are significantly higher than corresponding Fourier spectra in the high frequency range (10--1000 Hz). Comparing the two kinds of power density spectra may help to probe the intrinsic nature of timing phenomena in compact objects.

21 pages, 10 figures, to appear in Astrophysical Journal