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Impulse Response of an LTI System

Module by: Richard Baraniuk. E-mail the author

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Summary: An introduction to the impulse response of an LTI system.

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Figure 1. We will see:

  • Output of an LTI system ("at rest") is completely determined by the input and the response to an impulse.
  • Impulse response: Figure 2 and Figure 3.
Figure 1
Figure 1 (fig1.png)
Figure 2: δt δ t is the impulse input and ht h t is the impulse response.
Figure 2 (fig2.png)
Figure 3
(a) This "shocks" the system suddenly.(b) This is the response to the shock.
Figure 3(a) (fig31.png) Figure 3(b) (fig32.png)

Practical "impulses"

  • hammer blow to a structure
  • hand clap or gun blast in a room
  • air gun blast under water

How to Obtain the Impulse Response?

Theory

  1. Solve DE for yt y t with ft=δt f t δ t (see Lathi section 2.8 if interested).
  2. Use Laplace transforms (to come) (ELEC 301).

Practice

  1. Apply an impulse-line input signal to the system and measure the output.
  2. Fourier methods (to come).

For Now

Until Fourier Analysis of LSI Systems we will assume that ht h t is given. This means that the goal is now to compute output yt y t given ht h t and input ft f t (Figure 4).

Figure 4: hh is the impulse response.
Figure 4 (fig4.png)

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