Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

A universal two-way approach for estimating unknown frequencies for unknown number of sinusoids in a signal based on eigenspace analysis of Hankel matrix

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

We develop a novel approach to estimate the \(n\) unknown constituent frequencies of a noiseless signal that comprises of unknown number, \(n\), of sinusoids of unknown phases and unknown amplitudes. The new two-way approach uses two constraints to accurately estimate the unknown frequencies of the sinusoidal components in a signal. The new approach serves as a verification test for the estimated unknown frequencies through the estimated count of the unknown number of frequencies. The Hankel matrix, of the time domain samples of the signal, is used as a basis for further analysis in the Pisarenko harmonic decomposition. The new constraints, the existence factor and the component factor, have been introduced in the methodology based on the relationships between the components of the sinusoidal signal and the eigenspace of the Hankel matrix. The performance of the developed approach has been tested to correctly estimate any number of frequencies within a signal with or without a fixed unknown bias. The method has also been tested to accurately estimate the very closely spaced low frequencies.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Hsu, L., Ortega, R., Damm, G.: A globally convergent frequency estimator. IEEE Trans. Autom. Control 44(4), 698–713 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bodson, M., Douglas, S.: Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency. In: Proceedings of 13th IFAC World Conference, San Francisco, CA, 1–5 July 1996

  3. Regalia, P.A.: An improved lattice-based adaptive IIR notch filter. IEEE Trans. Signal Process. 39(9), 2124–2128 (1991)

    Article  Google Scholar 

  4. Marino, R., Tomei, P.: Global estimation of n unknown frequencies. IEEE Trans. Autom. Control 47(8), 1324–1328 (2002)

    Article  MathSciNet  Google Scholar 

  5. Marino, R., Tomei, P.: Global estimation of n unknown frequencies. In: Proceedings of the 39th IEEE Conference on Decision and Control, vol. 2, pp. 1143–1147 (2000)

  6. Marino, R., Tomei, P.: Global adaptive observers for nonlinear systems via filtered transformations. IEEE Trans. Autom. Control 37(8), 1239–1245 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  7. Horn, R.A., Jhonson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (2013)

    MATH  Google Scholar 

  8. Loizou, P.C.: Speech Enhancement: Theory and Practices, 2nd edn. CRC Press, Boca Raton (2013)

    Google Scholar 

  9. Chaparro, L.F.: Signals and Systems Using Matlab. Elsevier (2012). ISBN: 978-0-12-374716-7

  10. Lindfield, G.R., Penny, J.E.T.: Numerical Methods Using Matlab, 3rd edn. Academic Press, Orlando (2012)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering and Informatics, School of Electrical Engineering and Computer Science, University of Bradford, Bradford, UK

    Adeel Ahmed, Yim Fun Hu, James M. Noras & Prashant Pillai

Authors
  1. Adeel Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yim Fun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James M. Noras
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Prashant Pillai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adeel Ahmed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmed, A., Hu, Y.F., Noras, J.M. et al. A universal two-way approach for estimating unknown frequencies for unknown number of sinusoids in a signal based on eigenspace analysis of Hankel matrix. SIViP 10, 543–549 (2016). https://doi.org/10.1007/s11760-015-0770-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-015-0770-8

Keywords

Search

Navigation