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Fuzzy time quantization and local normalization for the direct spectral estimation from laser Doppler velocimetry data

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Abstract

An adaptation of the fuzzy slotting method and the local normalization to the direct type of power spectral estimation are given. Using experimentally obtained data, it is shown that the two optional processing methods have equivalent influence on the estimated turbulence spectra, for the two processing types, the direct spectral estimation and the slotting technique. The question about the estimation quality of the fuzzy slotting and the local normalization is not addressed here. However, it is shown that the impact of fuzzy time quantization on the spectral density is that of a low-pass filter of a \(\text {sinc}^2\) shape.

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Acknowledgments

The work of Bettina Frohnapfel, making the LDV and hot-wire data publicly available, is gratefully acknowledged.

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Authors and Affiliations

  1. Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

    Holger Nobach

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  1. Holger Nobach
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Correspondence to Holger Nobach.

Electronic supplementary material

Below is the link to the electronic supplementary material.

348_2015_2050_MOESM1_ESM.py

aslot.py — Python program of the slotting estimator including individual weighting or forward-backward inter-arrival time weighting and, optionally, local normalization and fuzzy slotting

348_2015_2050_MOESM2_ESM.py

adir.py — Python program of the direct estimator including individual weighting or forward-backward inter-arrival time weighting and temporal limitation of the correlation function, nominator correction, normalization with the correlation function of the sampling function or, optionally, local normalization and fuzzy time quantization

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Nobach, H. Fuzzy time quantization and local normalization for the direct spectral estimation from laser Doppler velocimetry data. Exp Fluids 56, 182 (2015). https://doi.org/10.1007/s00348-015-2050-3

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  • DOI: https://doi.org/10.1007/s00348-015-2050-3

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