Using variability related to families of spectral estimators for mixed random processesJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Publication VersionPublished Version
AbstractTraditionally, 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.
Citation InformationLi Wen, Changxue Wang and Peter J. Sherman. "Using variability related to families of spectral estimators for mixed random processes" Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME Vol. 123 Iss. 4 (2001) p. 572 - 584
Available at: http://works.bepress.com/peter_sherman/1/