
webmasternambisde 
1.2.2019 

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

Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using arrivaltime 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 forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival time suppressing errors due to possible long gaps in the data stream, shorten of the correlation function, Bessel's correction and, optionally, local normalization

Estimator for the temporal crosscorrelation 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 forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival 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
 cslotuniv.py  Python source code   cslot.pdf  A detailed description of the algorithm   cquantcoinc.py  A crosscorrelation and power spectral density estimator using arrivaltime quantization, for coincident data only!   cquantindep.py  A crosscorrelation and power spectral density estimator using arrivaltime quantization, for independent data only! 
Systematic list of all readytouse programs

Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using the direct spectral estimation (not recommended, arrivaltime quantization is faster) including individual weighting or forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival time suppressing errors due to possible long gaps in the data stream, normalization with the correlation function of the sampling function, shorten of the correlation function, Bessel's correction and, optionally, local normalization and fuzzy time quantization
 adir.py  Python source code   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 sampleandhold interpolation with refinement, Bessel's correction, with additional weights suppressing intervals between samples of more than five times the mean interarrival time and the according errors due to possible long gaps in the data stream and with a new modelfree noise reduction
 aint.py  Python source code   aint.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 slotting technique (not recommended, arrivaltime quantization is faster) incliding individual weighting or forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival time suppressing errors due to possible long gaps in the data stream, Bessel's correction and, optionally, local normalization and fuzzy slotting

Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using the arrivaltime 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 forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival time suppressing errors due to possible long gaps in the data stream, shorten of the correlation function, Bessel's correction and, optionally, local normalization
 aquant.py  Python source code   libLDV.c  C source code (ported from aquant.py, thanks Stephan Weiss)   aquant.pdf  A detailed description of the algorithm 

Estimator for the temporal crosscorrelation and for the power spectral density from laser Doppler data sets using the
direct spectral estimation including individual weighting or forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival time suppressing errors due to possible long gaps in the data stream, Bessel's correction and, optionally, local normalization and fuzzy time quantization
 cdircoinc.py  Python source code for an estimator for coincident twochannel data, eg. from twocomponent measurements (not recommended, arrivaltime quantization is faster) 
 cdirindep.py  Python source code for an estimator for independent twochannel data, eg. from transversal twopoint measurements (not recommended, arrivaltime 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 arrivaltime quantization is necessary. 
 cdir.pdf  A detailed description of the algorithm 

Estimator for the temporal crosscorrelation 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 twochannel data, eg. from twocomponent measurements (not recommended, insufficient
bias correction at low data rates) 
 cintindep.py  Python source code for an estimator for independent twochannel data, eg. from transversal twopoint 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 twochannel data, eg. coincident twocomponent measurements, independent measurements, eg. from transversal twopoint measurements or mixed independent and shifted dependent noncoincident measurements, eg. from longitudinal twopoint 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 

Estimator for the temporal crosscorrelation and for the power spectral density from laser Doppler data sets using the
slotting technique including individual weighting or forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival 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
 cslotcoinc.py  Python source code for an estimator for coincident twochannel data, eg. from twocomponent measurements (not recommended, arrivaltime quantization is faster) 
 cslotindep.py  Python source code for an estimator for independent twochannel data, eg. from transversal twopoint measurements (not recommended, arrivaltime quantization is faster) 
 cslotuniv.py  Python source code for an universal estimator, which can be used with all kinds of twochannel data, eg. coincident twocomponent measurements, independent measurements, eg. from transversal twopoint measurements or mixed independent and shifted dependent noncoincident measurements, eg. from longitudinal twopoint 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 

Estimator for the temporal crosscorrelation and for the power spectral density from laser Doppler data sets using
arrivaltime quantization including individual weighting or forwardbackward arrivaltime weighting with a maximum of five times the mean interarrival time suppressing errors due to possible long gaps in the data stream, Bessel's correction and, optionally, local normalization
 cquantcoinc.py  Python source code for an estimator for coincident twochannel data, eg. from twocomponent 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 twochannel data, eg. from transversal twopoint 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 twochannel data, eg. coincident twocomponent measurements, independent measurements, eg. from transversal twopoint measurements or mixed independent and shifted dependent noncoincident measurements, eg. from longitudinal twopoint 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. 
Supplementary material to publications
 Nobach H (2015): Corrections to the direct spectral estimation for laser Doppler data. Experiments in Fluids 56:109
 Nobach H (2015): A modelfree noise removal for the interpolation method of correlation and spectral estimation from laser Doppler data. Experiments in Fluids 56:100
 Nobach H (2015): LDAKorrelations und Spektralschätzung — Ein Zwischenstand. 23. Fachtagung "Lasermethoden in der Strömungsmesstechnik", 8.10. Sept. 2015, Dresden
 Nobach H (2015): Fuzzy time quantization and local normalization for the direct spectral estimation from laser Doppler velocimetry data. Experiments in Fluids 56:182
 Nobach H (2016): Present methods to estimate the crosscorrelation and crossspectral density for twochannel laser Doppler anemometry. Proc. of the 18th International Symposium on Applications of Laser Techniques to Fluid Mechanics, July 0407, 2016, Lisbon, Portugal
 Nobach H (2016): Methoden zur Schätzung der Kreuzkorrelationsfunktion und des Kreuzleistungsdichtespektrums aus zufällig abgetasteten LDADaten. 24. Fachtagung "Lasermethoden in der Strömungsmesstechnik", 6.8. Sept. 2016, Cottbus
 Nobach H, Damaschke N, Kühn V (2016): Methoden zur Schätzung der Autokorrelationsfunktion und des Leistungsdichtespektrums aus zufällig abgetasteten LaserDopplerDaten. XXX. Messtechnisches Symposium des Arbeitskreises der Hochschullehrer für Messtechnik, 15.16. Sept. 2016, Hannover
 Damaschke N, Kühn V, Nobach H (2018): A Fair Review of Nonparametric Biasfree Autocorrelation and Spectral Methods for Randomly Sampled Data in Laser Doppler Velocimetry Digital Signal Processing 76, pp. 2233
