Laser Doppler Data Processing  Techniques  ForwardBackward (Inter)ArrivalTime Weighting 

If the interarrival times as used for the calculation of the mean or the variance (${w}_{i}={t}_{i}{t}_{i1}$) are used as weighting factors for the estimation of the correlation function or that of the power spectral density, there will be a correlation between the respective time lags in the corresponding correlation function and the interarrival times. The reason for that is that a crossproduct of velocities contributing to the correlation function requires that the two samples have exactly the respective interarrival time. If ${u}_{i}$ and ${u}_{j}$ are two velocity samples at times ${t}_{i}$ and ${t}_{j}$, where ${t}_{i}<{t}_{j}$, then the interarrival weight of the second sample ${w}_{j}={t}_{j}{t}_{j1}$ interferes with the time lag ${t}_{j}{t}_{i}$ of the correlation function. Therefore, the usual interarrival times cannot be used directly as weighting factors for the correlation or the spectrum estimation. Instead, a crossproduct of two velocity samples ${u}_{i}$ and ${u}_{j}$ can use the two interarrival weights $$\begin{array}{cc}{w}_{i}={t}_{i}{t}_{i1}& \mathrm{(backwardinterarrivaltime)}\\ {w}_{j}={t}_{j+1}{t}_{j}& \mathrm{(forwardinterarrivaltime)}\end{array}$$where ${u}_{i}$ is assumed to be the first and ${u}_{j}$ is the second sample (${t}_{i}<{t}_{j}$). In that case, the arrival times are ordered as ${t}_{i1}<{t}_{i}<{t}_{j}<{t}_{j+1}$, and the two weights are independent of the interarrival time ${t}_{j}{t}_{i}$ of the two samples. However, also here, this weighting scheme works efficiently only at high enough data densities of the order of ten samples per integral timescale or larger. Therefore, TransitTime Weighting should generally be preferred. original papers (combined with local normalization and fuzzy slotting):
adapted to the direct spectral estimation: 