IMPLICATIONS OF LOW-PASS FILTERING ON POWER SPECTRA AND AUTOCORRELATION FUNCTIONS OF TURBULENT VELOCITY SIGNALS

Filtering either through the electronics of an instrument or through d igital procedure is performed routinely on geophysical data. When velo city fluctuations are measured in turbulent flows using electromagneti c current meters (ECMs), a built-in low-pass Butterworth filter of ord er 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 characteri stics of velocity signals, mainly on variance, power spectra, and corr elation analyses. Variance losses resulting from filtering can be impo rtant but will vary with the order n of the Butterworth filter, decrea sing as n increases. Knowing the filter response, it is possible to re construct the original signal spectrum to evaluate the effect of filte ring on variance and to allow comparisons between data collected with different instruments. The autocorrelation function also is affected b y 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 s ize and shape differences in ECM sensors and must be taken into accoun t in comparative studies.