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Application of nonlinear spectral analysis and signal reconstruction to laser Doppler velocimetry

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Spectral analysis is a useful tool in engineering applications but many practical problems are encountered in computing power spectral densities (PSD), particularly in laser Doppler velocimetry where data are irregularly sampled. Methods to compute PSD are usely based on discrete Fourier transforms such as FFT. A non linear spectral analysis approach is tested and found to give better results, particularly with short data records. Results are also quite promising when non linear spectral analysis is combined with signal reconstruction to process irregularly sampled data.

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  1. Bell, W. A. 1983: Spectral analysis algorithms for the laser velocimeter. AIAA J. 21, 714–719

  2. Beutler, F. J. 1976: On the truncation error of the cardinal sampling expansion. IEEE Trans. Inf. Theory 22, 568–573

  3. Boyer, L.; Searby, G. 1986: Random sampling: distorsion and reconstruction of velocity spectra from fast Fourier-transform analysis of the analog signal of a laser Doppler processor. J. Appl. Phys. 60, 2699–2707

  4. Bucchave, P.; George, W. K.; Lumley, J. L. 1979: The measurement of turbulence with the laser Doppler anemometer. Ann. Rev. Fluid Mech. 11, 443–503

  5. Chen, C. H. 1982: Non linear maximum entropy spectral analysis method for signal recognition. Chichester: Research Studies Press

  6. Clark, J. J.; Palmer, M. R.; Lawrence, P. D. 1985: A transformation method for the reconstruction of function from nonuniformly spaced samples. IEEE Trans. Acoust. Speech Signal Process 33, 1151–1165

  7. Gaster, M.; Roberts, J. B. 1977: Spectral analysis of randomly sampled records by a direct transform. Proc. R. Soc. Lond. Ser. A 354, 27–58

  8. Kay, S. M.; Marple, S. L. 1981: Spectrum analysis: A modern perspective. Proc. Inst. Electr. Eng. Part 11, 69, 1380–1419

  9. Kolodzy, P. J.; Edwards, R. V. 1986: Computation of the autocorrelation function of velocity fluctuations using a laser anemometer in a sparsely seeded flows. 3rd int. symp. on LDA, Lisbon, Portugal

  10. Lourenco, L.; Olivari, D.; Riethmuller, M. L. 1982: LDV data processing: Theoretical and experimental analysis of optimization of digital data acquisition for LDV data. 1st int. symp. on LDA, Lisbon, Portugal

  11. McLaughlin, D. K.; Tieferman W. G. 1973: Biasing correction for individual realization of laser anemometer measurements in turbulent flows. Phys. Fluids 16, 2082–2088

  12. Marvasti, F. 1986: Spectral analysis of random sampling and error free recovery by an iterative method. Trans. IECE Japan E69, 79–82

  13. Mayo, W. T. Jr. 1978: Spectrum measurements with laser velocimeters. Proc. of the dynamic flow conference, Denmark, 851–868

  14. Norsworthy, K. H. 1978: Fourier transformation and spectrum analysis of sparsely sampled signals. In: Proc. of 3rd int. workshop on laser velocimetry, July 11–13, pp. 315–327. New York: Hemisphere

  15. Oppenheim, A. V.; Shafer R. W. 1975: Digital signal processing. Englewood Cliffs: Prentice Hall

  16. Roberts, J. B.; Gaster, M. 1978: Rapid estimation of spectra from irregularly sampled records. Proc. Inst. Electr. Eng. Part 2, 125, 92–96

  17. Roberts, J. B.; Gaster, M. 1980: On the estimation of spectra from randomly sampled signals: a method of reducing variability. Proc. R. Soc. Lond. Ser. A 371, 235–258

  18. Roberts, J. B.; Downie, J.; Gaster, M. 1980: Spectral analysis of signals from a laser Doppler anemometer operating in the burst mode. J. Phys. E 13, 977–981

  19. Srikanataiah, D. W.; Coleman, H. W. 1985: Turbulence spectra from individual realization velocimetry data. Exp. Fluids 3, 35–44

  20. Tropea, C. D. 1987: Turbulence induced spectral bias in laser anemometry. AIAA J. 25, 306–311

  21. Veynante, D. 1985: Etude numérique et expérimentale d'une zone de mélange réactive. Ph.D. Thesis, Ecole Centrale des Arts et Manufactures

  22. Veynante, D.; Candel, S. M.; Martin, J. P. 1986: Influence of the System response on the coherent structures in a confined shear layer. Phys. Fluids 29, 3912–3914

  23. Weckman, E. J.; Sobesiak, A.; Tropea, C. D.; Brzutowski, T. A. 1986: LDA measurements in the base region of a pool fire. 3rd int. symp. on LDA, Lisbon, Portugal

  24. Wiley, R. G. 1978: Recovery of bandlimited signals from unequally spaced samples. IEEE Trans. Commun. 26, 135–137

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Veyuante, D., Candel, S.M. Application of nonlinear spectral analysis and signal reconstruction to laser Doppler velocimetry. Experiments in Fluids 6, 534–540 (1988). https://doi.org/10.1007/BF00196599

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  • Fourier
  • Fourier Transform
  • Spectral Analysis
  • Analysis Approach
  • Spectral Density