10/08 - Mechanics of Convolution & Fourier Transform: Difference between revisions
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|<math>=h(t)*x(t) \,\!</math> |
|<math>=h(t)*x(t) \,\!</math> |
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===Example 1=== |
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|<math>\delta(t)*x(t)\,\!</math> |
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|<math>=\int_{-\infty}^{\infty} \delta(\lambda)x(t-\lambda)\,d\lambda</math> |
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|<math>=x(t)\int_{-\infty}^{\infty} \,d\lambda</math> |
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|<math>=x(t)\,\!</math> |
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Revision as of 00:38, 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 | ||