10/3,6 - The Game: Difference between revisions
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(New page: ==The Game== The idea behind the game is to use linearity and time invariance to find an output for a given input. An initial input and output are given. {| border="1" cellpadding="5" cel...) |
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==The Game== |
==The Game== |
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The idea behind the game is to use linearity and time invariance to find an output for a given input. An initial input and output are given. |
The idea behind the game is to use linearity (superposition and proportionality) and time invariance to find an output for a given input. An initial input and output are given. |
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|<math> \Longrightarrow </math> |
|<math> \Longrightarrow </math> |
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|<math> x(\lambda)h(t-\lambda) \,\!</math> |
|<math> x(\lambda)h(t-\lambda) \,\!</math> |
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|Proportionality |
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|Linearity |
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|<math> x(t) = \int_{-\infty}^{\infty} x(\lambda) \delta (t-\lambda)\, dx</math> |
|<math> x(t) = \int_{-\infty}^{\infty} x(\lambda) \delta (t-\lambda)\, dx</math> |
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|<math> \Longrightarrow </math> |
|<math> \Longrightarrow </math> |
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|<math> \int_{-\infty}^{\infty} x(\lambda)h(t-\lambda)\, dx</math> |
|<math> \int_{-\infty}^{\infty} x(\lambda)h(t-\lambda)\, dx</math> |
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|Superposition |
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|Linearity |
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Revision as of 17:18, 11 November 2008
The Game
The idea behind the game is to use linearity (superposition and proportionality) and time invariance to find an output for a given input. An initial input and output are given.
| Input | LTI System | Output | Reason |
| Given | |||
| Time Invarience | |||
| Proportionality | |||
| Superposition |
