Frequency Domain I: Bode Plots and Transfer Functions

  • John Milton
  • Toru Ohira


Up to now, we have focused on descriptions of the dynamics of biological systems in the time domain, that is, on how variables change as a function of time. However, for certain types of problems, it is often more convenient to analyze dynamics in the frequency domain. For example, we typically describe the heartbeat in terms of frequency, namely, the number of beats per minute, rather than in terms of its period, i.e., the time between successive beats. In this chapter, we focus on the response of linear dynamical systems to sinusoidal inputs in the frequency domain. Sinusoidal inputs are of interest in the laboratory, since they are easy to implement. The responses provide an estimate of the linearity of the dynamical system, and they can be used to approximate the differential equation that is consistent with the observed input–output relationships.


Transfer Function Derivative Term Impulse Response Function Linear Dynamical System Sinusoidal Input 
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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

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