Frequency Domain II: Fourier Analysis and Power Spectra

  • John Milton
  • Toru Ohira


There are several practical problems associated with the use of the Laplace transform to study input–output relationships in the laboratory. In particular, it is extremely difficult to obtain the Laplace integral transform for measured signals, and even if the transform is known, obtaining the inverse transform can be problematic. At the root of these problems is the lack of efficient numerical methods to calculate the Laplace transform and its inverse [146].


Time Series Power Spectrum Fast Fourier Transform Fourier Series Power Spectral Density 
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. 35.
    J. S. Bendat and A. G. Piersol. Random data: Analysis and measurement procedures, 2nd ed. John Wiley & Sons, New York, 1986.MATHGoogle Scholar
  2. 52.
    W. E. Boyce and R. C. DiPrima. Elementary differential equations and boundary value problems, 9th ed. John Wiley & Sons, New York, 2005.Google Scholar
  3. 53.
    R. N. Bracewell. The Fourier transform and its applications, 2nd ed., revised. McGraw–Hill, San Francisco, 1986.Google Scholar
  4. 67.
    G. A. Bryant. Animal signals and emotion in music: coordinating affect across group. Frontiers in Psychology, 4:1–12, 2013.CrossRefGoogle Scholar
  5. 102.
    B. A. Cohen and A. Sances. Stationarity of the human electroencephalogram. Med. Biol. Eng. Comput., 15:513–518, 1977.CrossRefGoogle Scholar
  6. 108.
    J. W. Cooley and J. W. Tukey. An algorithm for machine calculation of complex Fourier series. Math. Computation, 19:297–301, 1965.MathSciNetCrossRefMATHGoogle Scholar
  7. 146.
    C. E. Epstein and J. Shotland. The bad truth about Laplace’s transform. SIAM Rev., 50:504–520, 2008.MathSciNetCrossRefMATHGoogle Scholar
  8. 172.
    A. S. French and A. V. Holden. Alias-free sampling of neuronal spike trains. Kybernetik, 5:165–171, 1971.CrossRefGoogle Scholar
  9. 176.
    V. Fugère and R. Krahe. Electric signals and species recognition in the wave-type gymnotiform fish Apteronotus leptorhynchus. J. Exp. Biol., 213:225–236, 2010.Google Scholar
  10. 191.
    W. B. Gearhart and H. S. Shultz. The function sinxx. The College Mathematics Journal, 21:90–99, 1990.Google Scholar
  11. 205.
    A. L. Goldberger, V. Bharagava, B. J. West, and A. J. Mandell. On the mechanism of cardiac electrical stability: the fractal hypothesis. Biophys. J., 48:525–528, 1985.CrossRefGoogle Scholar
  12. 272.
    J. D. Hunter, J. G. Milton, P. J. Thomas, and J. D. Cowan. Resonance effect for neural spike time reliability. J. Neurophysiol., 80:1427–1438, 1998.Google Scholar
  13. 313.
    F. M. Klis, A. Boorsma, and P. W. J. DeGroot. Cell wall construction in Saccharomycetes cerevisiae. Yeast, 23:185–202, 2006.Google Scholar
  14. 342.
    T. J. Lewis and M. R. Guevara. 1∕f power spectrum of the QRS complex does not imply fractal activation of the ventricles. Biophys. J., 60:1297–1300, 1991.CrossRefGoogle Scholar
  15. 402.
    G. Meyer-Kress, I. Choi, N. Weber, R. Bargas, and A. Hübler. Musical signals from Chua’s circuit. IEEE Trans. Circuits Systems II Analog Digital Signal Processing, 40:688–695, 1993.CrossRefGoogle Scholar
  16. 434.
    P. Moller. Electric fishes: History and behavior. Chapman & Hall, London, 1995.Google Scholar
  17. 463.
    E. Niedermeyer and F. Lopes da Silva. Electro-encephalography: Basic principles, clinical applications and related fields. Urban & Schwarzenberg, Baltimore, 1987.Google Scholar
  18. 475.
    K. Omori, H. Kojima, R. Kakani, D. H. Stavit, and S. M. Blaugrund. Acoustic characteristics of rough voice: subharmonics. J. Voice, 11:40–47, 1997.CrossRefGoogle Scholar
  19. 498.
    R. J. Peterka, A. C. Sanderson, and D. P. O’Leary. Practical considerations in the implementation of the French–Holden algorithm for sampling neuronal spike trains. IEEE Trans. Biomed. Engng., 25:192–195, 1978.CrossRefGoogle Scholar
  20. 505.
    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical recipes: The art of scientific computing, 3rd ed. Cambridge University Press, New York, 2007.Google Scholar
  21. 530.
    X. Rodet. Sound and music from Chua’s circuit. J. Circuits Systems Computers, 3:49–61, 1993.CrossRefGoogle Scholar
  22. 566.
    J. A. Simmons. Resolution of target range by echolocating bats. J. Acosut. Soc. Amer., 54:157–173, 1973.CrossRefGoogle Scholar
  23. 599.
    A. D. Straw, B. Branson, T. R. Neumann, and M. H. Dickinson. Multi-camera real-time three-dimensional tracking of multiple flying animals. J. Roy. Soc. Interface, 8:6900–6914, 2010.Google Scholar
  24. 629.
    W. van Drongelen. Signal processing for neuroscientists: Introduction to the analysis of physiological signals. Academic Press, New York, 2007.Google Scholar
  25. 672.
    H. Zakon, J. Oestreich, S. Tallarovic, and F. Triefenbach. EOD modulations of brown ghost electric fish: JARs, chirps, rises, and dips. J. Physiol. Paris, 96:451–458, 2002.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • John Milton
    • 1
  • Toru Ohira
    • 2
  1. 1.W.M. Keck Science DepartmentThe Claremont CollegesClaremontUSA
  2. 2.Graduate School of MathematicsNagoya UniversityNagoyaJapan

Personalised recommendations