10/3,6 - The Game: Difference between revisions
Jump to navigation
Jump to search
(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...) |
|||
| Line 1: | Line 1: | ||
==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. |
||
{| border="1" cellpadding="5" cellspacing="0" |
{| border="1" cellpadding="5" cellspacing="0" |
||
| Line 22: | Line 22: | ||
|<math> \Longrightarrow </math> |
|<math> \Longrightarrow </math> |
||
|<math> x(\lambda)h(t-\lambda) \,\!</math> |
|<math> x(\lambda)h(t-\lambda) \,\!</math> |
||
|Proportionality |
|||
|Linearity |
|||
|- |
|- |
||
|<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 |
|||
|Linearity |
|||
|} |
|} |
||
Revision as of 16:18, 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 |
