Document Type

Article

Publication Version

Published Version

Publication Date

12-2001

Journal or Book Title

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volume

123

Issue

4

First Page

572

Last Page

584

DOI

10.1115/1.1409257

Abstract

Traditionally, characterization of spectral information for wide sense stationary processes has been addressed by identifying a single best spectral estimator from a given family. If one were to observe significant variability in neighboring spectral estimators then the level of confidence in the chosen estimator would naturally be lessened. Such variability naturally occurs in the case of a mixed random process, since the influence of the point spectrum in a spectral density characterization arises in the form of approximations of Dirac delta functions. In this work we investigate the nature of the variability of the point spectrum related to three families of spectral estimators: Fourier transform of the truncated unbiased correlation estimator, the truncated periodogram, and the autoregressive estimator. We show that tones are a significant source of bias and variability. This is done in the context of Dirichlet and Fejer kernels, and with respect to order rates. We offer some expressions for estimating statistical and arithmetic variability. Finally, we include an example concerning helicopter vibration. These results are especially pertinent to mechanical systems settings wherein harmonic content is prevalent.

Comments

This article is from Journal of Dynamic Systems, Measurement and Control 123 (2001): 572, doi: 10.1115/1.1409257. Posted with permission.

Copyright Owner

ASME

Language

en

File Format

application/pdf

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