Estimation of power spectral density from laser Doppler data via linear interpolation and deconvolution

• Published in: Experiments in fluids Vol. 50; no. 1; pp. 179 - 188
• Main Authors: Moreau, S., Plantier, G., Valière, J.-C., Bailliet, H., Simon, L.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-01-2011; Springer; Springer Verlag (Germany)
• Subjects: Autocorrelation functions; Deconvolution; Density; Doppler effect; Engineering; Engineering Fluid Dynamics; Engineering Sciences; Engineering Thermodynamics; Exact sciences and technology; Fluid dynamics; Fluid flow; Fluid- and Aerodynamics; Fluids; Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Instrumentation for fluid dynamics; Lasers; Physics; Research Article; Signal and Image processing; Weighting Algorithm; Laser Doppler Anemometry Measurement; Power Spectral Density Estimation; Laser Doppler Anemometry; Power Spectral Density; Autocorrelation function; Deconvolution; Linear interpolation; Laser Doppler anemometers; Data processing; Velocity measurement; Performance
• ISSN: 0723-4864; 1432-1114
• DOI: 10.1007/s00348-010-0905-1

Spectral estimation of irregularly sampled velocity data issued from Laser Doppler Anemometry measurements is considered in this paper. A new method is proposed based on linear interpolation followed by a deconvolution procedure. In this method, the analytic expression of the autocorrelation function of the interpolated data is expressed as a linear function of the autocorrelation function of the data to be estimated. For the analysis of both simulated and experimental data, the results of the proposed method is compared with the one of the reference methods in LDA: refinement of autocorrelation function of sample-and-hold interpolated signal method given by Nobach et al. (Exp Fluids 24:499–509,
1998
), refinement of power spectral density of sample-and-hold interpolated signal method given by Simon and Fitzpatrick (Exp Fluids 37:272–280,
2004
) and fuzzy slotting technique with local normalization and weighting algorithm given by Nobach (Exp Fluids 32:337–345,
2002
). Based on these results, it is concluded that the performances of the proposed method are better than the one of the other methods, especially for what concerns bias and variance.