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TECHNICAL PAPERS

Using Variability Related to Families of Spectral Estimators for Mixed Random Processes

[+] Author and Article Information
Li Wen, Changxue Wang, Peter Sherman

Department of Aerospace Engineering and Engineering Mechanics, Iowa State University, Ames, IA 50011

J. Dyn. Sys., Meas., Control 123(4), 572-584 (Feb 21, 2001) (13 pages) doi:10.1115/1.1409257 History: Received February 21, 2001
Copyright © 2001 by ASME
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References

Figures

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(a) Comparison of statistical standard deviation of single order PER(n) and the averaged PER(n) spectral estimates for selected order n at nontone frequency f=0.1 Hz. (b) Comparison of statistical standard deviation of single order PER(n) and the averaged PER(n) spectral estimates for selected order n at tone frequency f=0.3 Hz.
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(a) Comparison of statistical standard deviation of single order AR(n) and the averaged AR(n) spectral estimates for selected order n at non-tone frequency f=0.1 Hz. (b) Comparison of statistical standard deviation of single order AR(n) and the averaged AR(n) spectral estimates for selected order n at tone frequency f=0.3 Hz.
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Arithmetic mean and 2-σ curves corresponding to use of a family of theoretical FT(n) spectra. [Note: Where not shown, the lower 2-σ curve is −∞.]
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(a) 2-σ curves for an average of 6 AR(n) spectra, n=5:1:10; (b) 2-σ curves for an average of 81 AR(n) spectra, n=20:1:100.
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Example of Dirichlet kernel for n=10, 20, and 30
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Average of FT(n) theoretical spectra for the range 1→nmax for nmax=100, 200 and 500
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(a) Example of Fejer kernel for n=10, 20 and 30 in dB; (b) comparison of the nth and the average of the first n Fejer’s kernels for n=100 and 1000.
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Arithmetic (a) mean and (b) standard deviation of collection of {AR(k): k=2,m} spectra for m=20, 40, 80, and 160
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(a) Comparison of simulation results against predictions (25) at tone’s frequency f=0.25 Hz, (b) Comparison of simulation results against predictions (25) at noise frequency f=0.1 Hz.
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(a) Evaluation of the variance expression in (28) as a function of model order at a noise frequency. Also shown is the estimated variability of the average of AR spectra (See Section 5 for related discussion). (b) Comparison of predicted (using (28)) 2-σ regions associated with an AR(40) model, and an average of AR(p) models for p=2:160. Also shown is the estimated variability of the average of AR spectra (see Section 5 for related discussion).
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(a) Comparison of 95% (or 2-σ) confidence interval of AR(n) for n=20 and 40 for Westland data, (b) Comparison of standard deviation of AR(n) spectral estimates for n=20 and 40 for Westland data.
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(a) Comparison of 95% (or 2-σ) confidence interval of PER(n) for n=256 and 1024 for Westland data. (b) Comparison of 2-sigma of PER(n) for n=256 and 1024 for Westland data.

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