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Fundamentals of Data Processing

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Springer Handbook of Experimental Fluid Mechanics

Part of the book series: Springer Handbooks ((SHB))

Abstract

In this chapter the fundamentals of statistical parameter estimation are reviewed for applications typical in experimental fluid mechanics. The chapter begins with a review of the probability density function and its moments and continues with common estimators for the mean and variance of stationary random processes. A brief introduction to signal noise is given as a prelude to a rigorous discussion of the Cramér–Rao Lower Bound (CRLB). The CRLB represents the lower bound of variance of unbiased estimators of a parameter. This concept is deepened using illustrations from the laser Doppler, phase Doppler and PIV measurement techniques. The chapter closes with a short discussion about the propagation of errors in a measurement chain.

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Abbreviations

ACF:

autocorrelation function

CRLB:

Cramér–Rao lower bound

ML:

maximum-likelihood

MLE:

maximum-likelihood estimator

PDF:

probability density function

PIV:

particle image velocimetry

PSD:

particle size distribution

PSD:

power spectral density

SNR:

signal-to-noise ratio

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Author information

Authors and Affiliations

  1. Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077, Göttingen, Germany

    Holger Nobach

  2. Fachgebiet Strömungslehre und Aerodynamik, Technische Universität Darmstadt, Petersenstraße 30, 64287, Darmstadt, Germany

    Cameron Tropea Dr.

Authors
  1. Holger Nobach
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  2. Cameron Tropea Dr.
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Corresponding authors

Correspondence to Holger Nobach or Cameron Tropea Dr. .

Editor information

Editors and Affiliations

  1. Fachgebiet Strömungslehre und Aerodynamik, Technische Universität Darmstadt, Petersenstraße 30, 64287, Darmstadt, Germany

    Cameron Tropea Dr.

  2. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor St., 60607-7022, Chicago, IL, USA

    Alexander L. Yarin Dr.

  3. Mechanical Engineering, Michigan State University, A118 Engineering Research Complex, 48824-1326, East Lansing, MI, USA

    John F. Foss Dr.

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© 2007 Springer-Verlag

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Nobach, H., Tropea, C. (2007). Fundamentals of Data Processing. In: Tropea, C., Yarin, A.L., Foss, J.F. (eds) Springer Handbook of Experimental Fluid Mechanics. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30299-5_23

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  • DOI: https://doi.org/10.1007/978-3-540-30299-5_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25141-5

  • Online ISBN: 978-3-540-30299-5

  • eBook Packages: EngineeringEngineering (R0)

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