Python programs for estimating correlation functions and the appropriate power spectral densities from irregularly sampled LDV data sets

Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using arrival-time quantization (recommended, because
from the signal theoretical point of view it is as efficient as the slotting technique and the direct spectral estimation,
but the fastest among these three) including normalization with the correlation function of the sampling function and individual weighting or forward-backward arrival-time weighting with a maximum of five times the mean inter-arrival time suppressing errors due to possible long gaps in the data stream, shorten of the correlation function, Bessel's correction and, optionally, local normalization

libLDV.c - C source code (ported from aquant.py, thanks Stephan Weiss)

aquant.pdf - A detailed description of the algorithm

Estimator for the temporal cross-correlation and for the power spectral density from laser Doppler data sets using the slotting technique (recommended, because this
is the only estimation technique that can correctly handle mixed independent and dependent measurements) including individual weighting or forward-backward arrival-time weighting with a maximum of five times the mean inter-arrival time suppressing errors due to possible long gaps in the data stream, a variable exponent of the product of the individual weights taking into account the fraction of dependent measurements among the data in each slot, Bessel's correction and, optionally, local normalization and fuzzy slotting

adir.pdf - A detailed description of the algorithm

Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using the interpolation method (not recommended, insufficient
bias correction at low data rates), namely the sample-and-hold interpolation with refinement, Bessel's correction, with additional weights suppressing intervals between samples of more than five times the mean inter-arrival time and the according errors due to possible long gaps in the data stream and with a new model-free noise reduction

aslot.pdf - A detailed description of the algorithm

Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using the arrival-time quantization (recommended, because
from the signal theoretical point of view it is as efficient as the slotting technique and the direct spectral estimation,
but the fastest among these three) including normalization with the correlation function of the sampling function and individual weighting or forward-backward arrival-time weighting with a maximum of five times the mean inter-arrival time suppressing errors due to possible long gaps in the data stream, shorten of the correlation function, Bessel's correction and, optionally, local normalization

cdircoinc.py - Python source code for an estimator for coincident two-channel data, eg. from two-component measurements (not recommended, arrival-time quantization is faster)

cdirindep.py - Python source code for an estimator for independent two-channel data, eg. from transversal two-point measurements (not recommended, arrival-time quantization is faster)

For data with mixed independent and dependent measurements with a certain delay between
the channels this estimation principle doesn't work. In this case, the arrival-time quantization is necessary.

cdir.pdf - A detailed description of the algorithm

Estimator for the temporal cross-correlation and for the power spectral density from laser Doppler data sets using the
interpolation method including Bessel's correction

cintcoinc.py - Python source code for an estimator for coincident two-channel data, eg. from two-component measurements (not recommended, insufficient
bias correction at low data rates)

cintindep.py - Python source code for an estimator for independent two-channel data, eg. from transversal two-point measurements (not recommended, insufficient
bias correction at low data rates)

cintuniv.py - Python source code for an universal estimator, which can be used with all kinds of two-channel data, eg. coincident two-component measurements, independent measurements, eg. from transversal two-point measurements or mixed independent and shifted dependent non-coincident measurements, eg. from longitudinal two-point measurements incl. variations of the preferred delay of the dependent measurements (not recommended, insufficient bias correction at low data rates, high computational costs)

cint.pdf - A detailed description of the algorithm

cslotcoinc.py - Python source code for an estimator for coincident two-channel data, eg. from two-component measurements (not recommended, arrival-time quantization is faster)

cslotindep.py - Python source code for an estimator for independent two-channel data, eg. from transversal two-point measurements (not recommended, arrival-time quantization is faster)

cslotuniv.py - Python source code for an universal estimator, which can be used with all kinds of two-channel data, eg. coincident two-component measurements, independent measurements, eg. from transversal two-point measurements or mixed independent and shifted dependent non-coincident measurements, eg. from longitudinal two-point measurements incl. variations of the preferred delay of the dependent measurements (recommended, because this is the only estimation technique that can correctly handle mixed independent and dependent measurements)

cslot.pdf - A detailed description of the algorithm

cquantcoinc.py - Python source code for an estimator for coincident two-channel data, eg. from two-component measurements (recommended, because from the signal theoretical point of view it is as efficient as the slotting technique and the direct spectral estimation, but the fastest among these three)

cquantindep.py - Python source code for an estimator for independent two-channel data, eg. from transversal two-point measurements (recommended, because from the signal theoretical point of view it is as efficient as the slotting technique and the direct spectral estimation, but the fastest among these three)

cquantuniv.py - Python source code for an universal estimator, which can be used with all kinds of two-channel data, eg. coincident two-component measurements, independent measurements, eg. from transversal two-point measurements or mixed independent and shifted dependent non-coincident measurements, eg. from longitudinal two-point measurements incl. variations of the preferred delay of the dependent measurements (not recommended, because this estimation technique can't correctly handle mixed independent and dependent measurements)

This procedure is similar to the direct estimation (cdir.pdf) with quantized
arrival times.