Studies of the daily variation of cosmic ray intensity by power spectral techniques have been essentially limited in the past to demonstrating the existence of peaks at frequencies corresponding to the 24-hour (diurnal) wave and its harmonics. The Fourier analysis technique has largely been used in many detailed investigations of the daily variation. A recent comparative study of both techniques over five solar rotations has revealed the correspondence between the two techniques and the suitability of the power spectral method in relating cosmic ray observations to interplanetary parameters. The study of the daily variation of the cosmic ray intensity over a long interval, extending, for example, over the 11-year solar cycle, is complicated by other types of superposed variations. An analysis of real data can be considerably facilitated by a power spectral study using simulated input incorporating different artificial but physically based variations. The present study utilizes, in the simulation data, the known average characteristics of the daily variation as well as other variations present in real data. Power spectra are then calculated from a series of test data sets, each of which consists of hourly values for an interval of 27 days. The essential parameters relating to the peaks of the daily variations are tabulated. The study demonstrates the effects of superposed variations (starting from the simple case of a pure sinusoid) on power spectral features. The ambient power (background power level under the diurnal peak) is found to be dependent on the day-to-day phase changes in the daily variation. The realistic magnitude of the random noise is observed to have large observable effects in the power at the high frequencies only.