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Tests for Randomness, Stationarity, Normality and Comparison of Spectra

Report Number: AFFDL TR 65-74
Author(s): J. S. Bendat; L. D. Enochson; A. G. Piersol
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1965-08
Pages: 54
Contract: AF 33(615)-1314
Project: 4437
Task: 443706
AD Number: AD0621906

This report contains material for carrying out certain practical tests for randomness, stationarity, and normality of physical data, as well as details on how to test for equivalence of two power spectral density functions. The tests for randomness are qualitative inspections of measured properties from sample records, such as power spectra, probability density, auto-correlation functions, which may be part of a regular data reduction procedure. The tests for stationarity are nonparametric statistical procedures, based upon Run and Trend Distributions, which require simple quantitative calculations for acceptance or rejection. The test for normality is a statistical hypothesis test based upon sample measurements of the amplitude probability density function at seven equispaced amplitude levels from zero to plus and minus three sigma. To test for equivalence of two spectra, a straight-forward procedure is recommended which requires knowledge only of the number of degrees-of-freedom associated with the spectral estimates, and the full bandwidth occupied by the data. A special case of this procedure is to compare an unknown spectrum to a 'white' spectrum.

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