Power Spectrum Representation for Nonstationary Random Vibration

Abstract A unified theory for the power spectral representation of nonstationary random processes is presented. The principal properties of two time-dependent spectrum definitions, the physical spectrum and the instantaneous spectrum, are reviewed with emphasis placed on difficulties brought about by the uncertainty principle. The exact relationship between these two spectrum definitions is shown to be, in a certain sense, a generalization to nonstationary processes of the Wiener-Khintchine theorem. Expressions for the physical and instantaneous spectra of a pair of beating sinusoids are derived, plotted, and discussed in relation to the uncertainty principle. Simple, general expressions for the instantaneous and physical spectra of the uniformly modulated process and for the mean-square system response to the uniformly modulated process are derived and discussed.

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