Abstract
A variety of methods have been developed to obtain acurate frequency estimates from laser Doppler velocimetry (LDV) signals. Rapid scanning and fiber optic LDV systems require robust methods for extracting accurate frequency estimates with computational efficiency from data with poor signal-to-noise ratios. These methods typically fall into two general categories, time domain parametric techniques and frequency domain techniques. The frequency domain approach is initiated by transforming the Doppler bursts into the frequency domain using the fast Fourier transform (FFT). From this basic transformation a variety of interpolation procedures (parabolic, Gaussian, and centroid fits) have been developed to optimize the frequency estimation accuracy. The time domain approaches are derived from the parametric form of a sinusoid. The estimation of constants in this relationship is performed to satisfy specific constraints, typically a minimization of a variance expression. A comparison of these techniques is presented using simulated signals and additive Gaussian and Poisson white noise. The statistical bias and random errors for each method are presented from 200 signal simulations at each condition. Frequency estimation via the FFT with zero-padding and a Gaussian interpolation scheme was found to produce the lowest bias and random errors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A(z) :
-
eigenfilter or characteristic polynomial
- a m + 1 :
-
eigenvector
- f :
-
frequency, Hz
- f :
-
normalized frequency f = f/f s
- \(\hat f\) d :
-
Doppler frequency estimate
- f i :
-
frequency of FFT spectral bin
- f s :
-
sampling frequency
- N :
-
number of sample points in data set
- P i :
-
ith power spectral line from PSD
- r xx (i):
-
autocorrelation coefficient for time lag i
- RMn + 1 :
-
autocorrelation matrix of order M+1
- T :
-
sampling period
- Δ f :
-
spectral resolution for FFT, Δ f = 1/N Δt
- Δt :
-
sampling interval
References
Aktar, M.; Sankur, B.; Istefanopulos, Y. 1985: Properties of the maximum likelihood and Pisarenko spectral estimates. Signal Processing 8, 401–413
Bachalo, W. D.; Werthimer, D.; Raffanti, R.; Hermes, R. J. 1989: A high speed Doppler signal processor of frequency and phase measurements. Third Int. Conf. on Laser Anemometry — Advances and Applications (ed. Turner, J.), Univ. of Manchester, Swansea
Dantec Inc. 1987: Burst Spectrum Analyzer: Instruction Manual. Siemens, Munich, FRG
Harris, F. J. 1978: On the use of windows for harmonic analysis with the discrete Fourier transdorm. Proc. of the IEEE 66, 51–83
Hayes, M. H.; Clements, M. A. 1986: An efficient algorithm for computing Pisarenko's harmonic decomposition using Levinson's recursion. IEEE Trans. ASSP, ASSP-34, no. 3, 485–491
Hishida, K.; Kobashi, K.; Maeda, M. 1989: Improvement of LDA/PDA using a digital signal processor (DSP). Third Int. Conf. on Laser Anemometry — Advances and Applications (ed. Turner, J.), Univ. of Manchester, Swansea, paper S. 2
Ibrahim, K. M.; Werthimer, G. D.; Bachalo, W. D. 1990: Signal processing considerations for laser Doppler and phase Doppler applications. Presented at 5th Int. Sym. on Application of Laser Techniques to Fluid Mechanics Workshop on the use of Computers in Flow measurements, Lisbon, Portugal
Kalb, H. T.; Crosswy, F. L. 1983: Discrete Fourier transform signal processor for laser-Doppler anemometry. AEDC-TR-83–46, Arnold Engineering Development Center AAFS, Tennessee
Kay, S. M.; Marple, S. L. 1981: Spectrum analysis — a modern perspective. Proc. IEEE 69, 1380–1419
Marple, S. L. Jr.; 1987: Digital Spectral Analysis with Applications, Englewood Cliffs/NJ: Prentice-Hall
Matovic, D.; Tropea, I. C.; Martinuzzi, R. 1987: Frequency estimation of LDA signals by model parametric estimation. In: The use of computers in laser velocimetry, (eds. Pfeifer, H. I; Jaeggy, B.), Inst. St. Louis Report R/05/87
Matovic, D.; Tropea, I. C. 1990: An Adaptive Spectral Peak Interpolation with Application to LDA Signal Processing: Laser Anemometry Advances and Application, (eds. Dybbs, Alexander; Bahman, Ghurashi), ASME, 653–663
Pisarenko, V. F. 1973: The retrieval of harmonics from a covariance function. Geophys. J. Roy. Astron. Soc. 33, 347–366
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. 1987: Numerical Recipes. New York: Cambridge University Press
Rife, D. C.; Boorstyn, R. R. 1974: Single-tone parameter estimation from discrete-time observations, IEEE Trans, on Information Theory 20, 591–598
Shinpaugh, K. A. 1989: Design of a rapidly scanning 3-D laser Doppler velocimeter with low SNR signal processing. M. S. Thesis, Dept. Aero. Engr., VPI & SU
Shinpaugh, K. A.; Simpson, R. L.; Wicks, A. L.; Fleming, J. L. 1990: Signal processing techniques for low signal-to-noise ratio laser Doppler velocimetry signals. Fifth Int. Symp. on Appl. of Laser Anemometry to Fluid Mech., Lisbon, Portugal
TSI Inc. 1986: Laser Velocimetry Systems: Product Information. St. Paul, Minnesota
Wriedt, T.; Bauckhage, K. A.; Schone, A. 1989: Application of Fourier analysis to phase-Doppler-signals generated by rough metal particles. IEEE Trans. on Instrumentation and Measurement 38, 984–990
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shinpaugh, K.A., Simpson, R.L., Wicks, A.L. et al. Signal-processing techniques for low signal-to-noise ratio laser Doppler velocimetry signals. Experiments in Fluids 12, 319–328 (1992). https://doi.org/10.1007/BF00187310
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00187310