10/08 - Mechanics of Convolution & Fourier Transform: Difference between revisions
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==Convolution: A visual approach== |
==Convolution: A visual approach== |
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*Flip: |
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*Shift: |
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*Multiply: |
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*Add/Integrate: |
Revision as of 14:44, 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
- 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.
Convolution: A visual approach
- Flip:
- Shift:
- Multiply:
- Add/Integrate: