Time-Domain Analysis

Time-Domain Analysis

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In this chapter we have consolidated the mathematical developments necessary to relate the physical system and the differential equation describing it. This included the derivation of the impulse response, step response, and convolution integral. These quantities, which are important to the theory of filtering, were shown to be a function of the L.I. solutions of the homogeneous equation. It is hoped that this time-domain approach has clarified the transition from the basic differential equation concepts to the everyday tools of the linear system analyst.

Chapter Contents:

  • 1.1 Definitions
  • 1.2 The Differential Equation
  • 1.3 Solution of the Homogeneous Equation
  • 1.4 Solution of the Nonhomogeneous Equation
  • 1.4.1 Specific Case
  • 1.4.2 More General Case
  • 1.5 Convolution Integral
  • 1.6 Impulse Function
  • 1.7 Step Function
  • 1.8 Impulse Response, Step Response, and Weighting Function
  • 1.9 Summary
  • References
  • Problems

Inspec keywords: convolution; transient response; time-domain analysis; step response; filtering theory; linear systems; differential equations

Other keywords: differential equation; filtering theory; linear system; time-domain approach; L.I. solutions; impulse response; convolution integral; step response; homogeneous equation

Subjects: Differential equations (numerical analysis); Filtering methods in signal processing; Signal processing theory; Differential equations (numerical analysis)

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