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We review the problem of spectral estimation from velocity data sampled irregularly in time by a laser Doppler anemometer (LDA) from very early estimators based on slot correlation to more refined estimators, which build upon a signal reconstruction and an equidistant re-sampling in time. The discussion is restricted to single realization anemometry, i.e. excluding multiple particle signals. We classify the techniques and make an initial assessment before describing currently used methods in more detail. An intimately related subject, the simulation of LDA data, is then briefly reviewed, since this provides a means of evaluating various estimators. Using the expectation and variance as figures of merit, the advantages and disadvantages of several estimators for varying types of turbulent velocity spectral distributions are discussed. A set of recommendations is put forward as a conclusion.

The estimation of turbulence power spectra from randomly sampled laser Doppler anemometer (LDA) data can be done via the autocorrelation function (ACF) approach, whereby the slotting technique has the advantage that the ACF can be estimated at any data rate. Two improvements on Mayo's slotting technique for estimating the ACF, `local normalization' and the `fuzzy slotting technique', were proposed and compared in a benchmark test. However, it proved possible to merge these approaches and the resulting algorithm produced correlation coefficients with a lower variance than either of the individual algorithms. This lower variance in the ACF estimates can then be capitalized upon in order to produce better estimates of the turbulence power spectrum.

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