Implications of low-pass filtering on power spectra and autocorrelation functions of turbulent velocity signals |
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| Institution: | (1) Département de géographie, Université de Montréal, C.P. 6128, succ. Centre-ville, H3C 3J7 Montréal, Québec, Canada;(2) Department of Geography, McGill Uníversíty, 805 Sherbrooke Street West, H3A 2K6 Montreal, Quebec, Canada |
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| Abstract: | Filtering either through the electronics of an instrument or through digital procedure is performed routinely on geophysical
data. When velocity fluctuations are measured in turbulent flows using electromagnetic current meters (ECMs), a builtin lowpass
Butterworth filter of order n usually attenuates fluctuations at high frequencies. However, the effects of this filter may
not be acknowledged in turbulence studies, thus impeding comparisons between data collected with different ECMs. This paper
explores the implications of the filters on the characteristics of velocity signals, mainly on variance, power spectra, and
correlation analyses. Variance losses resulting from filtering can be important but will vary with the order n of the Butterworth
filter, decreasing as n increases. Knowing the filter response, it is possible to reconstruct the original signal spectrum
to evaluate the effect of filtering on variance and to allow comparisons between data collected with different instruments.
The autocorrelation function also is affected by filtering which increases the value of the coefficients in the first lags,
resulting in an overestimation of the integral length scale of coherent structures. These important effects add to those related
to size and shape differences in ECM sensors and must be taken into account in comparative studies. |
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| Keywords: | Butterworth filters time-series analysis turbulence statistics defiltering Electromagnetic Current Meters (ECMs) |
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