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Times and Sines: Fourier Analysis

  • Nicolaas Westerhof
  • Nikolaos Stergiopulos
  • Mark I. M. Noble
Chapter

Abstarct

Fourier analysis breaks a periodic signal up in a series of sine waves, called ­harmonics. Any repetitive physiological signal, such as pressure or flow in the steady state can be written as a Fourier series:
$$ f(t)=\frac{{a}_{0}}{2}+{\displaystyle \sum _{n=1}^{N}[{a}_{n}\mathrm{cos}\frac{2pt}{T}+{b}_{n}\mathrm{sin}\frac{2p}{T}t],}\text {n harmonic number},\text {and N}\ge 0$$

Keywords

Heart Rate Fourier Analysis Fourier Series Phase Angle Sine Wave 
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.

References

  1. 1.
    Westerhof N, Sipkema P, Elzinga G, Murgo JP, Giolma JP. Arterial impedance. In: Hwang NHC, Gross DR, Patel DJ. Quantitative cardiovascular studies. 1979, Baltimore, MD; University Park Press.Google Scholar
  2. 2.
    Hamming RW. Digital filters. 1977, Englewood Cliffs, NJ, Prentice Hall.Google Scholar
  3. 3.
    Stergiopulos N, Meister J-J, Westerhof N. Scatter in the input impedance spectrum may result from the elastic nonlinearity of the arterial wall. Am J Physiol 1995;269:H1490–H1495.PubMedGoogle Scholar
  4. 4.
    Murgo JP, Westerhof N, Giolma JP, Altobelli SA. Aortic input impedance in normal man: relationship to pressure wave forms. Circulation 1980;62:105–116.PubMedCrossRefGoogle Scholar

Copyright information

© Springer US 2010

Authors and Affiliations

  • Nicolaas Westerhof
    • 1
  • Nikolaos Stergiopulos
    • 2
  • Mark I. M. Noble
    • 3
  1. 1.Departments of Physiology and Pulmonology ICaR-VUVU University Medical CenterAmsterdamthe Netherlands
  2. 2.Laboratory of Hemodynamics and Cardiovascular TechnologySwiss Federal Institute of TechnologyLausanneSwitzerland
  3. 3.Cardiovascular MedicineAberdeen UniversityAberdeenScotland

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