Present methods to estimate the cross-correlation and cross-spectral density for two-channel laser Doppler anemometry

For the estimation of the autocorrelation and the auto-spectral density from irregularly sampled laser Doppler data sets three types of estimators are known, the slotting technique, the direct spectral estimation and the interpolation with filter correction. In this paper similar estimation techniques are discussed for the cross-correlation and the cross-spectral density case of two randomly sampled laser Doppler data sets. Appropriate estimators are derived for different sampling characteristics of the two data sets, namely for the coincident sampling, the independent sampling and for a mixed sampling of independent and dependent measurements including a certain delay between dependent measurements in the two data channels.