Abstract
A procedure to estimate and remove the contribution of data noise to the correlation function and the power spectral density calculated from laser Doppler data with the interpolation method is introduced. In comparison with earlier approaches, the new procedure is model free and, therefore, more objective. The new procedure is proven based on experimental data taken with a laser Doppler system, where the power spectral density obtained with the interpolation method is compared directly to data from a hot-wire reference measurement.
References
Adrian RJ, Yao CS (1987) Power spectra of fluid velocities measured by laser Doppler velocimetry. Exp Fluids 5:17–28
Buchhave P, Velte CM (2015) Reduction of noise and bias in randomly sampled power spectra. Exp Fluids 56:79. doi:10.1007/s00348-014-1674-z
Buchhave P, George WK Jr, Lumley JL (1979) The measurement of turbulence with the laser Doppler anemometer. In: Annual Review of Fluid Mechanics, vol 11. Annual Reviews Inc, Palo Alto, CA, pp 442–503
Gaster M, Roberts JB (1975) Spectral analysis of randomly sampled signals. J Inst Math Appl 15:195–216
Gaster M, Roberts JB (1977) The spectral analysis of randomly sampled records by a direct transform. Proc R Soc Lond A 354:27–58
George WK (1988) Quantitative measurement with the burst-mode laser Doppler anemometer. Exp Therm Fluid Sci 1:29–40
George WK, Beuther PD, Lumley JL (1978) Processing of random signals. In: Proceedings of the dynamic flow conference, Skovlunde, Denmark, (PO Box 121, DK-2740 Skovlunde), pp. 757–800
Gjelstrup P, Nobach H, Jørgensen F, Meyer KE (2000) Experimental verification of novel spectral analysis algorithms for laser Doppler anemometry data. In: Proc. 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal. Paper 3.2
Mayo WT Jr (1974) A discussion of the limitations and extensions of power spectrum estimation with burst counter LDV systems. In: Proceedings of the second international workshop on laser Velocimetry, (Bull. No. 144), Purdue Univ., West Lafayette, Ind, pp. 90–104
Mayo WT Jr, Shay MT, Ritter S (1974) The development of new digital data processing techniques for turbulence measurements with a laser velocimeter. USAF Arnold Engineering Development Center Report No. AEDC-TR-74-53
Moreau S, Plantier G, Valière JC, Bailliet H, Simon L (2011) Estimation of power spectral density from laser Doppler data via linear interpolation and deconvolution. Exp Fluids 50:179–188
Nobach H (1999) Processing of stochastic sampled data in laser Doppler anemometry. In: Proceedings of 3rd International Workshop on Sampling Theory and Applications, Loen, Norway, pp. 149–154
Nobach H (2000) A global concept of autocorrelation and power spectral density estimation from LDA data sets. In: Proceedings of 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal. Paper 3.5
Nobach H (2002) Local time estimation for the slotted correlation function of randomly sampled LDA data. Exp Fluids 32:337–345
Nobach H (2015) Corrections to the direct spectral estimation for laser Doppler data. Exp Fluids. doi:10.1007/s00348-015-1980-0
Nobach H, Müller E, Tropea C (1998a) Correlation estimator for two-channel, non-coincidence laser-Doppler-anemometer. In: Proceedings of 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal. Paper 32.1
Nobach H, Müller E, Tropea C (1998b) Efficient estimation of power spectral density from laser Doppler anemometer data. Exp Fluids 24:499–509
Roberts JB, Ajmani DBS (1986) Spectral analysis of randomly sampled signals using a correlation-based slotting technique. IEE Proc 133(2):153–162
Scott PF (1974) Random sampling theory and its application to laser velocimeter turbulent spectral measurements. Tech. rep., General Electric Co., Corporate Res. and Development. Report No. 74CRD216, Tech, Info Series
Scott PF (1976) Distortion and estimation of the autocorrelation function and spectrum of a randomly sampled signal. Ph.D. thesis, Rensselear Polytechnic Institute, Troy, NY
Shay MT (1976) Digital estimation of autocovariance functions and power spectra from randomly sampled data using a lag product technique. Ph.D. Thesis, Texas A&M University, College Station, TX
Simon L, Fitzpatrick J (2004) An improved sample-and-hold reconstruction procedure for estimation of power spectra from LDA data. Exp Fluids 37:272–280
Tummers MJ, Passchier DM, Aswatha Narayana PA (1995) LDA measurements of time- and spatial correlation functions in an adverse pressure gradient wake. In: Proceedings of ASME/JSME Fluids Engineering and Laser Anemometry Conference, Hilton Head Island, South Carolina, USA. FED-Vol. 229, pp. 347–355
van Maanen HRE, Tummers MJ (1996) Estimation of the autocorrelation function of turbulent velocity fluctuations using the slotting technique with local normalization. In: Proceedings of 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal. Paper 36.4
van Maanen HRE, Nobach H, Benedict LH (1999) Improved estimator for the slotted autocorrelation function of randomly sampled LDA data. Meas Sci Technol 10(1):L4–L7
Velte CM, George WK, Buchhave P (2014) Estimation of burst-mode LDA power spectra. Exp Fluids 55:1674. doi:10.1007/s00348-014-1674-z
Acknowledgments
The work of Palle Gjelstrup, Finn E. Jørgensen (Dantec Dynamics) and Knud Erik Meyer (Danmarks Tekniske Universitet) performing the experiments and providing the data is gratefully acknowledged.
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Nobach, H. A model-free noise removal for the interpolation method of correlation and spectral estimation from laser Doppler data. Exp Fluids 56, 100 (2015). https://doi.org/10.1007/s00348-015-1975-x
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DOI: https://doi.org/10.1007/s00348-015-1975-x