10/08 - Mechanics of Convolution & Fourier Transform: Difference between revisions
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*How can we do this without using the flip shift multiply integrate? |
*How can we do this without using the flip shift multiply integrate? If <math> u(t) \,\!</math> isn't involved, then you can plug n chug with the integral. The u(t) will change the limits, which can be impractical to evaulate if you have more than 2. |
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*Go over the flip shift multiply integrate. Make sure you can do it "visually" |
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==Convolution: A visual approach== |
Revision as of 14:43, 14 November 2008
Mechanics of the Convolution
Remember from the game:
Input | LTI System | Output | Reason |
Given | |||
Time Invarience | |||
Proportionality | |||
Superposition |
We will also denote the convolution as
Communative Property
Let thus | ||
The order of integration switched due to changing from | ||
Example 1
Example 2
- How can we do this without using the flip shift multiply integrate? If isn't involved, then you can plug n chug with the integral. The u(t) will change the limits, which can be impractical to evaulate if you have more than 2.