Times and Sines: Fourier Analysis

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


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:
$$ f(t)=\frac{{a}_{0}}{2}+{\displaystyle \sum _{n=1}^{N}[{a}_{n}\mathrm{cos}\frac{2pt}{T}+{b}_{n}\mathrm{sin}\frac{2p}{T}t],}\text {n harmonic number},\text {and N}\ge 0$$


Heart Rate Fourier Analysis Fourier Series Phase Angle Sine Wave 
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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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