Skip to main content
SpringerLink
Log in

Fast computation of spectral centroids

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

The spectral centroid of a signal is the curve whose value at any given time is the centroid of the corresponding constant-time cross section of the signal’s spectrogram. A spectral centroid provides a noise-robust estimate of how the dominant frequency of a signal changes over time. As such, spectral centroids are an increasingly popular tool in several signal processing applications, such as speech processing. We provide a new, fast and accurate algorithm for the real-time computation of the spectral centroid of a discrete-time signal. In particular, by exploiting discrete Fourier transforms, we show how one can compute the spectral centroid of a signal without ever needing to explicitly compute the signal’s spectrogram. We then apply spectral centroids to an emerging biometrics problem: to determine a person’s heart and breath rates by measuring the Doppler shifts their body movements induce in a continuous wave radar signal. We apply our algorithm to real-world radar data, obtaining heart- and breath-rate estimates that compare well against ground truth.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bizarro, J.P.S.: On the behavior of the continuous-time spectrogram for arbitrarily narrow windows. IEEE Trans. Signal Process. 55, 1793–1802 (2007)

    Article  MathSciNet  Google Scholar 

  2. Bizarro, J.P.S., Figueiredo, A.C.: The Wigner distribution as a toll for time–frequency analysis of fusion plasma signals: application to broadband reflectometry data. Nucl. Fusion 39, 61–82 (1999)

    Article  Google Scholar 

  3. Chen, K.-M., Misra, D., Wang, H., Chuang H.-R., Postow, E.: An X-band microwave life-detection system. IEEE Trans. Biomed. Eng. 33, 697–701 (1986)

    Article  Google Scholar 

  4. Chen, K.-M., Huang Y., Zhang J., Norman, A.: Microwave life-detection systems for searching human subjects under earthquake rubble or behind barrier. IEEE Trans. Biomed. Eng. 47, 105–114 (2000)

    Article  Google Scholar 

  5. Chen, J., Huang, Y., Li, Q., Paliwal, K.K.: Recognition of noisy speech using dynamic spectral subband centroids. IEEE Signal Process. Lett. 11, 258–261 (2004)

    Article  Google Scholar 

  6. Claasen, T.A.C.M., Mecklenbräuker, W.F.G.: The Wigner distribution—a tool for time–frequency signal analysis, Part II: discrete-time signals. Philips J. Res. 35, 276–300 (1980)

    MathSciNet  MATH  Google Scholar 

  7. Claasen, T.A.C.M., Mecklenbräuker, W.F.G.: The Wigner distribution—a tool for time–frequency signal analysis, Part III: relations with other time–frequency signal transformations. Philips J. Res. 35, 372–389 (1980)

    MathSciNet  MATH  Google Scholar 

  8. Cohen, L.: Time–frequency Analysis. Prentice Hall, Englewood Cliffs (1995)

    Google Scholar 

  9. Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  10. Feichtinger, H.G., Gröchenig, K., Strohmer, T.: Efficient numerical methods in non-uniform sampling theory. Numer. Math. 69, 423–440 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gajic, B., Paliwal, K.K.: Robust speech recognition in noisy environments based on subband spectral centroid histograms. IEEE Trans. Audio, Speech Lang. Process. 14, 600–608 (2006)

    Article  Google Scholar 

  12. Gatesman, A.J., Danylov, A., Goyette, T.M., Dickinson, J.C., Giles, R.H., Goodhue, W., Waldman, J., Nixon W.E., Hoen, W.: Terahertz behavior of optical components and common materials. Proc. SPIE 6212(62120E), 1–12 (2006)

    Google Scholar 

  13. Gröchenig, K.: Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type. Math. Comput. 68, 749–765 (1999)

    Article  MATH  Google Scholar 

  14. Massar, M.L.: Time–frequency analysis of terahertz radar signals for rapid heart and breath rate detection. M.S. Thesis, Air Force Institute of Technology (2008)

  15. Petkie, D.T., Bryan, E., Benton, C., Phelps, C., Yoakum, J., Rogers, M., Reed, A.: Remote respiration and heart rate monitoring with millimeter-wave/terahertz radars. Proc. SPIE 7117(71170I), 1–6 (2008)

    Google Scholar 

  16. Schubert, E., Wolfe, J.: Does timbral brightness scale with frequency and spectral centroid? Acta Acustica United with Acustica 92, 820–825 (2006)

    Google Scholar 

  17. Seo, J.S., Jin, M., Lee, S., Jang, D., Lee, S., Yoo, C.D.: Audio fingerprinting based on normalized spectral subband moments. IEEE Signal Process. Lett. 13, 209–212 (2006)

    Article  Google Scholar 

  18. Strohmer, T.: Computationally attractive reconstruction of bandlimited images from irregular samples. IEEE Trans. Image Process. 6, 540–548 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, Dayton, OH, 45433, USA

    Melody L. Massar & Matthew Fickus

  2. Department of Physics, Wright State University, Dayton, OH, 45435, USA

    Erik Bryan & Douglas T. Petkie

  3. Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson Air Force Base, Dayton, OH, 45433, USA

    Andrew J. Terzuoli Jr.

Authors
  1. Melody L. Massar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthew Fickus
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erik Bryan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Douglas T. Petkie
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Andrew J. Terzuoli Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matthew Fickus.

Additional information

Communicated by Qiyu Sun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Massar, M.L., Fickus, M., Bryan, E. et al. Fast computation of spectral centroids. Adv Comput Math 35, 83–97 (2011). https://doi.org/10.1007/s10444-010-9167-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10444-010-9167-y

Keywords

Search

Navigation