Investigation of spectral analysis techniques for randomly sampled velocimetry data

It is well known that velocimetry (LV) generates individual realization velocity data that are randomly or unevenly sampled in time. Spectral analysis of such data to obtain the turbulence spectra, and hence turbulence scales information, requires special techniques. The 'slotting' technique of Mayo et al, also described by Roberts and Ajmani, and the 'Direct Transform' method of Gaster and Roberts are well known in the LV community. The slotting technique is faster than the direct transform method in computation. There are practical limitations, however, as to how a high frequency and accurate estimate can be made for a given mean sampling rate. These high frequency estimates are important in obtaining the microscale information of turbulence structure. It was found from previous studies that reliable spectral estimates can be made up to about the mean sampling frequency (mean data rate) or less. If the data were evenly samples, the frequency range would be half the sampling frequency (i.e. up to Nyquist frequency); otherwise, aliasing problem would occur. The mean data rate and the sample size (total number of points) basically limit the frequency range. Also, there are large variabilities or errors associated with the high frequency estimates from randomly sampled signals. Roberts and Ajmani proposed certain pre-filtering techniques to reduce these variabilities, but at the cost of low frequency estimates. The prefiltering acts as a high-pass filter. Further, Shapiro and Silverman showed theoretically that, for Poisson sampled signals, it is possible to obtain alias-free spectral estimates far beyond the mean sampling frequency. But the question is, how far? During his tenure under 1993 NASA-ASEE Summer Faculty Fellowship Program, the author investigated from his studies on the spectral analysis techniques for randomly sampled signals that the spectral estimates can be enhanced or improved up to about 4-5 times the mean sampling frequency by using a suitable prefiltering technique. But, this increased bandwidth comes at the cost of the lower frequency estimates. The studies further showed that large data sets of the order of 100,000 points, or more, high data rates, and Poisson sampling are very crucial for obtaining reliable spectral estimates from randomly sampled data, such as LV data. Some of the results of the current study are presented.