Frequency Tracking with Spline Based Chirp Atoms

  • Matthias Wacker
  • Miroslav Galicki
  • Herbert Witte
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6134)


The tracking of prominent oscillations with time-varying frequencies is a common task in many signal processing applications. Therefore, efficient methods are needed to meet precision and run-time requirements. We propose two methods that extract the energy of the time frequency plane along a cubic spline trajectory. To raise efficiency, a sparse sampling method with dynamically shaped atoms is developed for the one method in contrast to standard Gabor atoms for the other. Numerical experiments using both synthetic and real-life data are carried out to show that dynamic atoms can significantly outperform classical Gabor formulations for this task.


Active Contour Model Spline Curve Dynamic Atom Alpha Oscillation Time Frequency Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Prudat, Y., Vesin, J.-M.: Multi-signal extensions of adaptive frequency tracking algorithms. Signal Processing 89, 963–973 (2009)zbMATHCrossRefGoogle Scholar
  2. 2.
    Johansson, A.T., White, P.R.: Instantaneous frequency estimation at low signal-to-noise ratios using time-varying notch filters. Signal Processing 88, 1271–1288 (2008)zbMATHCrossRefGoogle Scholar
  3. 3.
    Streit, R., Barrett, R.: Frequency line tracking using hidden markov models. IEEE Transactions on Acoustics, Speech and Signal Processing 38(4), 586–598 (1990)CrossRefGoogle Scholar
  4. 4.
    Witte, H., Putsche, P., Hemmelmann, C., Schelenz, C., Leistritz, L.: Analysis and modeling of time-variant amplitude-frequency couplings of and between oscillations of EEG bursts. Biological Cybernetics 99(2), 139–157 (2008)zbMATHCrossRefGoogle Scholar
  5. 5.
    Gabor, D.: Theory of communication. Journal of Institution of Electrical Engineers 93, 429–457 (1946)Google Scholar
  6. 6.
    Schoenberg, I.J.: On equidistant cubic spline interpolation. Bulletin of the Americal Mathematical Society 77(6), 1039–1044 (1971)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kováčová, M., Kristeková, M.: New version of matching pursuit decomposition with correct representation of linear chirps. In: Proceedings of Algoritmy, pp. 33–41 (2002)Google Scholar
  8. 8.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  9. 9.
    Schwab, K., Ligges, C., Jungmann, T., Hilgenfeld, B., Haueisen, J., Witte, H.: Alpha entrainment in human electroencephalogram recordings. Neuroreport 17, 1829–1833 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Matthias Wacker
    • 1
  • Miroslav Galicki
    • 1
  • Herbert Witte
    • 1
  1. 1.Institute for Medical Statistics, Computer Sciences and DocumentationFriedrich-Schiller-University Jena, GER 

Personalised recommendations