10/08 - Mechanics of Convolution & Fourier Transform: Difference between revisions
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===Example 2=== |
===Example 2=== |
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|<math>=\int_{-\infty}^{\infty} [u(\lambda)-u(\lambda-1)] \cdot [u(t-\lambda-1)-u(t-\lambda-3)]\,d\lambda</math> |
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|<math>=</math> |
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*How can we do this without using the flip shift multiply integrate? I can't visualize every problem unfortunately. |
Revision as of 01:40, 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? I can't visualize every problem unfortunately.