Skip to main content
SpringerLink
Log in

Frequency and Time—Frequency Domain Analysis Tools in Measurement

  • Chapter
  • First Online:
Data Modeling for Metrology and Testing in Measurement Science

Summary

A traditional approach to signal processing has been, for a long time, the frequency domain analysis, in which time or space periodicities can be identified. It is a relatively simple approach which usually carries significant information, suitable both as a first-step approach for further signal processing and for feature extraction. Because this approach carries no time information, frequency and time-domain analysis based on wavelets has become increasingly important. This shares a similar analytical approach making use of time-limited functions as the basis of the transform, allowing for space or time localization of short-lived repeating patterns. These are signal-processing tools which require some good understanding of the underlying theory to avoid common pitfalls and circumvent some limitations. Examples are given to show applicability.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. L. Angrisani, and M. D’Arco. A measurement method based on a modified version of the chirplet transform for instantaneous frequency estimation.IEEE Transactions on Instrumentation and Measurement, 51(4):704–711, 2002.

    Article  Google Scholar 

  2. L. Angrisani, P. Daponte, and M. D’Apuzzo. A method for the automatic detection and measurement of transients. Part i: The measurement method.Measurement, 25(1):19–30, 1999.

    Article  Google Scholar 

  3. L. Angrisani, P. Daponte, M. D’Apuzzo, and A. Testa. A measurement method based on the wavelet transform for power quality analysis.IEEE Transactions on Power Delivery, 13(4):990–998, 1998.

    Article  Google Scholar 

  4. A. N. Akansu, and R. A. Haddad.Multiresolution Signal Decomposition. Academic Press, San Diego, CA, 1992.

    MATH  Google Scholar 

  5. P.M. Bentley, and J.T.E. McDonnell. Wavelet transforms: An introduction.Electronics & Communication Engineering Journal, 6(4):175–186, 1994.

    Article  Google Scholar 

  6. J. W. Cooley, and J. W. Tukey. An algorithm for the machine calculation of complex Fourier series.Mathematics of Computation, 19:297–301, 1965.

    Article  MATH  MathSciNet  Google Scholar 

  7. I. Daubechies.Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, Philadelphia, 1992.

    MATH  Google Scholar 

  8. J. P. G. Lejeune Dirichlet. Sur la convergence des séries trignométriques que servent á représenter une fonction arbitraire entre des limites données.Journal de Crelle, 4:157–169, 1829.

    Google Scholar 

  9. P. Daponte, G. Mercurio, and S. Rapuano. A wavelet networks-based method for the digital telecommunication system monitoring.IEEE Transactions on Instrumentation and Measurement, 50(6):1773–1780, 2001.

    Article  Google Scholar 

  10. J.-B. J. Fourier.The Analytical Theory of Heat. Cambridge Press, London, 1878.

    Google Scholar 

  11. IEEE. Standard for terminology and test methods for analog-to-digital converters. Standard 1241, IEEE, 2001.

    Google Scholar 

  12. S. G. Johnson, and M. Frigo. A modified split-radix fft with fewer arithmetic operations.IEEE Transactions on Signal Processing, 55(1):111–119, 2007.

    Article  MathSciNet  Google Scholar 

  13. L. Angrisani, P. Daponte, and M. D’Apuzzo. A method for the automatic detection and measurement of transients. Part ii: Applications.Measurement, 25(1):31–40, 1999.

    Article  MATH  Google Scholar 

  14. H. Nyquist. Certain topics in telegraph transmission theory.Transactions AIEE, 47:617–644, 1928.

    Google Scholar 

  15. A. V. Oppenheim, R. W. Schafer, and J. R. Buck.Discrete-Time Signal Processing. Prentice Hall, Upper Saddle River, NJ, 1999.

    Google Scholar 

  16. C. Petrarca, and G. Lupo. Wavelet packet denoising of partial discharge data.Proceedings of 2006 IEEE Conference on Electrical Insulation and Dielectric Phenomena, pages 644–647, 2006.

    Google Scholar 

  17. O. Rioul. A discrete-time multiresolution theory.IEEE Transactions on Signal Processing, 41(8):2591–2606, 1993.

    Article  MATH  Google Scholar 

  18. O. Rioul, and M. Vetterli. Wavelets and signal processing.IEEE Signal Processing Magazine, pages 14–38, Oct 1991.

    Google Scholar 

  19. C. E. Shannon. Communication in the presence of noise.Proceedings Institute of Radio Engineers, 37(1):10–21, 1949.

    Google Scholar 

  20. R. G. Stockwell, L. Mansinha, and R. P. Lowe. Localization of the complex spectrum: The s transform.IEEE Transactions on Signal Processing, 44(4):998–1001, 1996.

    Article  Google Scholar 

  21. M. Vetterli, and C. Herley. Wavelets and filter banks: Theory and design.IEEE Transactions on Signal Processing, 40(9):2207–2232, September 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Telecomunicações, Instituto Superior Técnico, DEEC, UTL, Av. Rovisco Pais 1 1049-001 Lisbon, Portugal

    Pedro M. Ramos & Raul C. Martins

  2. Departement of Engineering, Universitá del Sannio, 82100 Benevento, Italy

    Sergio Rapuano & Pasquale Daponte

Authors
  1. Pedro M. Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raul C. Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergio Rapuano
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pasquale Daponte
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pedro M. Ramos .

Editor information

Editors and Affiliations

  1. Metrologica (INRIM), Divisione Termodinamica, Istituto Nazionale di Ricerca, Strada delle Cacce 73, Torino, 10135, Italy

    Franco Pavese

  2. MSC , Module 13 , National Physics Laboratory , Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom

    Alistair B. Forbes

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Birkhäuser Boston

About this chapter

Cite this chapter

Ramos, P.M., Martins, R.C., Rapuano, S., Daponte, P. (2009). Frequency and Time—Frequency Domain Analysis Tools in Measurement. In: Pavese, F., Forbes, A. (eds) Data Modeling for Metrology and Testing in Measurement Science. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4804-6_6

Download citation

Publish with us

Policies and ethics

Search

Navigation