Spectral analysis of biased LDA data

The spectral density function of turbulent velocity fluctuations can be estimated from randomly sampled LDA data by first computing a discretized autocorrelation function (using the slotting technique) followed by a Fourier transform of this function. The spectral estimates obtained in this way have a large statistical scatter in the high-frequency range. This work focuses on a spectral estimator with a much reduced statistical scatter (approximately 1 decade), enabling the retrieval of the spectral density function up to higher frequencies. This spectral estimator is based on a modification of the standard slotting technique, known as `local scaling' or `local normalization', in conjunction with a window of variable width. A series of benchmark tests for spectral estimators indicated that this estimator yields good overall results. This paper explores the characteristics of the new spectral estimator with regard to the effects of velocity bias and the presence of uncorrelated noise in the velocity data.