On various definitions of the envelope of a random process. (English) Zbl 1235.70189

Summary: Statistical properties of the envelope deefinitions of Rice, Crandall and Mark and Dugundji are derived and compared. It is shown that the definitions of Rice and Dugudji are equivalent, which implies that the envelope of Rice is independent of the choice of a central frequency. This contradicts results which have appeared in the literature and the reason for this contradiction is explained. The envelopes of Crandall and Mark and Dugundji are found to have the same first order probability density function but different crossing rates and mean frequencies.


70L05 Random vibrations in mechanics of particles and systems
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