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Metrology and Measurement Systems

The Journal of Committee on Metrology and Scientific Instrumentation of Polish Academy of Sciences

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Volume 18, Issue 4


Frequency and Damping Estimation Methods - An Overview

Tomasz Zieliński
  • Department of Telecommunications, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Krzysztof Duda
  • Department of Measurement and Instrumentation, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2011-12-25 | DOI: https://doi.org/10.2478/v10178-011-0051-y

Frequency and Damping Estimation Methods - An Overview

This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.

Keywords: damped sinusoids; frequency estimation; damping estimation; linear prediction; subspace methods; interpolated DFT

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About the article

Published Online: 2011-12-25

Published in Print: 2011-01-01

Citation Information: Metrology and Measurement Systems, Volume 18, Issue 4, Pages 505–528, ISSN (Print) 0860-8229, DOI: https://doi.org/10.2478/v10178-011-0051-y.

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