On the frequency scaling in continuous-time modeling

Rik Pintelon, Istvan Kollár

Research output: Contribution to journalArticle

35 Citations (Scopus)


When identifying continuous-time systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transfer function. Although the optimal scaling depends on the system, the model, and the excitation signal, the arithmetic mean of the maximum and minimum angular frequencies in the frequency band of interest is commonly used as a good compromise as shown in the following references: J. Schoukens and R. Pintelon, Identification of Linear Systems: A Practical Guideline to Accurate Modeling (London, U.K.: Pergamon), R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach, (Piscataway, N J: IEEE Press, 2001), and I. Kollár, R. Pintelon, Y. Rolain, J. Schoukens, G. Simon, " Frequency domain system identification toolbox for Matlab: Automatic processes - From data to model," in Proc. 13th IFAC Symp. System Identification, Rotterdam, The Netherlands, Aug. 27-29, 2003, pp. 1502-1506. In this paper, we show: 1) that the optimal frequency scaling also strongly depends on the estimation algorithm and 2) that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean.

Original languageEnglish
Pages (from-to)318-321
Number of pages4
JournalIEEE Transactions on Instrumentation and Measurement
Issue number1
Publication statusPublished - Jan 1 2005



  • Continuous-time modeling
  • Frequency domain
  • System identification

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering

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