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Impulse Response of an LTI System

Module by: Richard Baraniuk

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

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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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