Time- and Frequency-Domain Characteristics of Linear Time-Invariant Systems

  • Jan Willem Polderman
  • Jan C. Willems
Part of the Texts in Applied Mathematics book series (TAM, volume 26)


The purpose of this chapter is twofold. First, we explain how a linear time-invariant system acts in the frequency domain. An important feature of such systems is that (in an input/output setting) they transform sinusoidal (and, more generally, exponential) inputs into sinusoidal (exponential) outputs. This leads to the transfer function and the frequency response as a convenient way of describing such systems. The second purpose of this chapter is to study properties of the time- and frequency-domain response. Thus we describe important characteristics of a system that can be deduced from its step-response, or from its Bode and Nyquist plots.


Transfer Function Nyquist Plot Settling Time Step Response Exponential Behavior 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Jan Willem Polderman
    • 1
  • Jan C. Willems
    • 2
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  2. 2.Mathematics InstituteUniversity of GroningenGroningenThe Netherlands

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