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Graphical Understanding of Convolution

Module by: Richard Baraniuk. E-mail the author

Summary: An module concerning the graphical understanding of convolution.

Note:

Extremely tricky - be on your toes!!!
This helps when signals to convolve become complicated.
c⁢t=∫−∞∞f⁢τ⁢g⁢t−τd τ c t τ f τ g t τ
(1)

Notes:

  1. Integration is with respect to τ τ ( t t is a constant inside)
  2. With respect to τ τ g g is time reversed, g⁢−τ g τ and shifted right by t t
    Figure 1
    Figure 1 (fig1.png)
    An easy way to check: compare points to g⁢0 g 0 .

Example 1

Figure 2
Figure 2 (fig2.png)

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