Implications of low-pass filtering on power spectra and autocorrelation functions of turbulent velocity signals

TLDR: In this article, the authors explored the implications of the filters on the characteristics of velocity signals, mainly on variance, power spectra, and correlation analyses, and showed that the effect of the filter response on the original signal spectrum can be evaluated.

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.