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Summary: Convolution

Module by: Richard Baraniuk

Summary: A summary of the key concepts of convolution.

Figure 1
fig1.png

Problem:

Given H H and f f , compute y y.
  • Solution 1: Solve DE defined by H H for y y in terms of f f. (Resolve for each new f f)
  • Solution 2: Find impulse response h h
    Figure 2
    fig2.png
    Now y y is given by convolution of f f and h h yt=∫-∞∞fτht-τdτ y t τ f τ h t τ (Repeat just this for each new f f)

Note:

DE and impulse response h h are equivalent characterizations for all LTI systems!!!

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