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Forces on a Cylinder Suspended in Water

Keywords: time series, mixed spectra, filtering


The data give time series measurements on waves emanating from a cylinder suspended in a tank of water. The waves are believed to show a high frequency vibration, which is an artifact of the experiment equipment, as well as lower frequency vibration which reflects forces acting on the cylinder. It is of interest to identify and to filter out the high frequency vibration.

Variable Description

Waves Relative vertical displacement at equi-spaced times


Data File (tab-delimited text)


Newton, H. Joseph (1988). TIMESLAB: A time series analysis laboratory. Wadsworth, Pacific Grove, California, page 290.
Smyth, G. K. (2000). Employing symmetry constraints for improved frequency estimation by eigenanalysis methods. Technometrics 42, 277-289. (Abstract - Zipped Postscript)


Time series plot of the data:

waves1.gif (10174 bytes)


The series appears to have a continuous spectrum, expect for a high frequency spike:

> spec.pgram(Waves,span=8,plot=T)

waves2.gif (11550 bytes)


It is also possible to pick out the high frequency vibration using a discrete spectrum approach on a shortened series:

> out4 <- pronyfreq(Waves[1:50],nfreq=4,constant=F)
> out4$freq/2/pi
[1] 0.03635873 0.06433893 0.08958704 0.36787400

The first 3 frequencies here reflect the smooth peak in the periodogram, while the frequency at 0.37 is the spike in the periodogram.



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