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Linear Systems

  • Ram P. Kanwal

Abstract

Recall that we define a function as a rule that maps (transforms) numbers into numbers, whereas a functional maps functions into numbers. An operator maps functions into functions. Let a class of functions be given, all defined for a variable, say, time t, -∞ <t < ∞. Then an operator (transformation) L assigns a member of this class (inputs, excitations, or signals) to members of a second class of functions (outputs or responses). We shall use the symbol x(t) for an input and y(t) for the corresponding output. A system is a mathematical model of a physical device and is represented by an operator L. Then y(t) is called the response of x(t) due to the given system. A system is often represented by a box as shown in Figure 14.1.

Keywords

Linear System Impulse Response Step Response Impulse Response Function Sampling Theorem 
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.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Ram P. Kanwal
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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