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| 22.9.2022 |
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Python programs for estimating correlation functions and the appropriate power spectral densities from irregularly sampled LDV data sets
Recommended ready-to-use programs
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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
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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
 | cslotuniv.py - Python source code |  | cslot.pdf - A detailed description of the algorithm | | cquantcoinc.py - A crosscorrelation and power spectral density estimator using arrival-time quantization, for coincident data only! | | cquantindep.py - A crosscorrelation and power spectral density estimator using arrival-time quantization, for independent data only! |
Systematic list of all ready-to-use programs
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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
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Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using the slotting technique (not recommended, arrival-time quantization is faster) incliding 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, Bessel's correction and, optionally, local normalization and fuzzy slotting
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Estimator for the temporal autocorrelation and for the power spectral density from laser Doppler data sets using the direct spectral estimation (not recommended, arrival-time quantization is faster) 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, 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
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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
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Estimator for the temporal cross-correlation and for the power spectral density from laser Doppler data sets using
arrival-time quantization 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, Bessel's correction and, optionally, local normalization
| 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. |
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Estimator for the temporal cross-correlation and for the power spectral density from laser Doppler data sets using the
slotting technique 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
| 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 |
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Estimator for the temporal cross-correlation and for the power spectral density from laser Doppler data sets using the
direct spectral estimation 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, Bessel's correction and, optionally, local normalization and fuzzy time quantization
| cdircoinc.py - Python source code for an estimator for coincident two-channel data, e.g. 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 |
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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 |
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 model-free noise removal for the interpolation method of correlation and spectral estimation from laser Doppler data. Experiments in Fluids 56:100
- Nobach H (2015): LDA-Korrelations- 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 cross-correlation and cross-spectral density for two-channel laser Doppler anemometry. Proc. of the 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, July 04-07, 2016, Lisbon, Portugal
- Nobach H (2016): Methoden zur Schätzung der Kreuzkorrelationsfunktion und des Kreuzleistungsdichtespektrums aus zufällig abgetasteten LDA-Daten. 24. Fachtagung "Experimentelle Strömungsmechanik", 6.-8. Sept. 2016, Cottbus
- Nobach H, Damaschke N, Kühn V (2016): Methoden zur Schätzung der Autokorrelationsfunktion und des Leistungsdichtespektrums aus zufällig abgetasteten Laser-Doppler-Daten. 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 Non-parametric Bias-free Autocorrelation and Spectral Methods for Randomly Sampled Data in Laser Doppler Velocimetry. Digital Signal Processing 76, pp. 22-33
- Damaschke N, Kühn V, Nobach H (2018): A direct spectral estimation method for laser Doppler data using quantization of arrival times. Proc. of the 19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, July 16-19, 2018, Lisbon, Portugal
- Nobach H, Damaschke N, Kühn V (2018): Ein fairer Vergleich von Methoden zur Autokorrelations- und Leistungsdichteschätzung aus Laser-Doppler-Daten. 26. Fachtagung "Experimentelle Strömungsmechanik", 4.-6. Sept. 2018, Rostock
- Nobach H, Damaschke N, Kühn V (2019): Korrektur dynamischer Fehler für direkte Spektralschätzung von ungleichmä&sylig;ig abgetasteten Daten inklusive korrelierter Abtastintervalle. 27. Fachtagung "Experimentelle Strömungsmechanik", 3.-5. Sept. 2019, Erlangen
- Damaschke N, Kühn V, Nobach H (2021): Bias Correction for Direct Spectral Estimation from Irregularly Sampled Data Including Sampling Schemes with Correlation. Journal on Advances in Signal Processing 2021, 7
- Nobach H, Damaschke N, Kühn V (2021): Korrelations- und Spektralschätzung aus LDA-Daten — ein genauerer Blick. 28. Fachtagung "Experimentelle Strömungsmechanik", 7.-9. Sept. 2021, Bremen
- Diaz L., Nobach H (2022): Korrelationsfunktion und Leistungsspektrum von fast periodischen Signalen nicht vollständiger Perioden. 29. Fachtagung "Experimentelle Strömungsmechanik", 6.-8. Sept. 2022, Ilmenau
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