(New page: Here's the problem: <math>\,Input \rightarrow SYSTEM \rightarrow Output</math> :* <math>\,e^{2jt} \rightarrow SYSTEM \rightarrow te^{-2jt}</math> :* <math>\,e^{-2jt} \rightarrow SYSTEM \...) |
|||
| Line 5: | Line 5: | ||
:* <math>\,e^{2jt} \rightarrow SYSTEM \rightarrow te^{-2jt}</math> | :* <math>\,e^{2jt} \rightarrow SYSTEM \rightarrow te^{-2jt}</math> | ||
:* <math>\,e^{-2jt} \rightarrow SYSTEM \rightarrow te^{2jt}</math> | :* <math>\,e^{-2jt} \rightarrow SYSTEM \rightarrow te^{2jt}</math> | ||
| + | |||
| + | |||
| + | From the information given above, it seems like the system takes an input <math>\,x(t)</math> and transforms in into an output <math>\,y(t) = tx(-t)</math> | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | For an input <math>\,x(t) = cos(2t)</math> | ||
| + | |||
| + | :<math>\,cos(2t) \rightarrow SYSTEM \rightarrow tcos(-2t)</math> | ||
| + | |||
| + | Thus, <math>\,y(t) = tcos(-2t)</math> | ||
Latest revision as of 05:17, 17 September 2008
Here's the problem:
$ \,Input \rightarrow SYSTEM \rightarrow Output $
- $ \,e^{2jt} \rightarrow SYSTEM \rightarrow te^{-2jt} $
- $ \,e^{-2jt} \rightarrow SYSTEM \rightarrow te^{2jt} $
From the information given above, it seems like the system takes an input $ \,x(t) $ and transforms in into an output $ \,y(t) = tx(-t) $
For an input $ \,x(t) = cos(2t) $
- $ \,cos(2t) \rightarrow SYSTEM \rightarrow tcos(-2t) $
Thus, $ \,y(t) = tcos(-2t) $
