A comprehensive study of the bias and variance of frequency-response-function measurements: Optimal window selection and overlapping strategies

  • Authors:

  • Jérôme Antoni;Johan Schoukens

  • Affiliations:

  • Laboratoire Roberval de Mécanique, University of Technology of Compiègne, 60205 Compiègne, France;Vrije Universiteit Brussel, Department ELEC, Pleinlaan2, B1050 Brussels, Belgium

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2007

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Abstract

This paper investigates the measurement errors involved in measuring frequency response functions from weighted-overlapped segment averaging, a technique that has become a standard in modern spectral analysers due to its computational advantages. A particular attention is paid to leakage errors, for which this procedure has been frequently criticised. Exact and asymptotic expressions for the bias and variance are provided, whose minimisation enables the derivation of the optimal settings to be used with this procedure. Our main finding is that a Half-sine or Diff window with 23 overlap achieves the best compromise to reduce leakage errors, and this is independently of the system frequency response function. This conclusion is to be contrasted with the customary habit of using a Hanning window with 12 overlap.