Spectral estimation using a variable window and the slotting technique with local normalization

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Abstract
The autocorrelation function of turbulent velocity fluctuations can be estimated from randomly sampled LDA data using the slotting technique. However, the autocorrelation function (acf) obtained in this way suffers from a relatively high statistical variance. This paper proposes a modification to the slotting technique that results in a much lower statistical variance at small lag times. The modification enables a direct estimation of the Taylor microscale from the curvature of the acf at zero lag time. The potential of the modified slotting technique for the estimation of spectral density functions is also explored. It is shown that the modified slotting technique in conjunction with a variable window forms a powerful spectral estimator for low data density flows.

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