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A new technique for computation of cross-power spectral density of random processes has been developed, programmed, and tested on a variety of constructed random and periodic signals of known characteristics. The technique is based on derived relationships between cross-power spectral density and the mean value of certain products of a random signal and the response of an oscillator driven by the random signal. In addition, a technique for discrimination between periodic and random signals has been developed that is based on comparison of the amplitude distribution of the signal and the amplitude distribution of the acceleration of an oscillator driven by the signal. Computations have been performed for a variety of signals with known characteristics with very satisfactory results.