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== | ||
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> | ||
|<math> x(\lambda)h(t-\lambda) \,\!</math> | |<math> x(\lambda)h(t-\lambda) \,\!</math> | ||
| | |Proportionality | ||
|- | |- | ||
|<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> | ||
|<math> \Longrightarrow </math> | |<math> \Longrightarrow </math> | ||
|<math> \int_{-\infty}^{\infty} x(\lambda)h(t-\lambda)\, dx</math> | |<math> \int_{-\infty}^{\infty} x(\lambda)h(t-\lambda)\, dx</math> | ||
| | |Superposition | ||
|} | |} | ||
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 |