(New page: ==Problem== A linear system’s response to <math>e^{2jt}</math> is <math>te^{-2jt}</math>, and its response to <math>e^{-2jt}</math> is <math>te^{2jt}</math>. What is the system’s respo...) |
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==Problem== | ==Problem== | ||
A linear system’s response to <math>e^{2jt}</math> is <math>te^{-2jt}</math>, and its response to <math>e^{-2jt}</math> is <math>te^{2jt}</math>. What is the system’s response to <math>cos(2t)</math>? | A linear system’s response to <math>e^{2jt}</math> is <math>te^{-2jt}</math>, and its response to <math>e^{-2jt}</math> is <math>te^{2jt}</math>. What is the system’s response to <math>cos(2t)</math>? | ||
| + | |||
| + | ==Solution== | ||
| + | If the system is linear, then the following is true: | ||
| + | |||
| + | For <math>x_{1}(t)\rightarrow y_{1}(t)</math> | ||
| + | and <math>x_{2}(t)\rightarrow y_{2}(t)</math> | ||
| + | |||
| + | then | ||
| + | |||
| + | <math>axi</math> | ||
Revision as of 19:52, 16 September 2008
Problem
A linear system’s response to $ e^{2jt} $ is $ te^{-2jt} $, and its response to $ e^{-2jt} $ is $ te^{2jt} $. What is the system’s response to $ cos(2t) $?
Solution
If the system is linear, then the following is true:
For $ x_{1}(t)\rightarrow y_{1}(t) $ and $ x_{2}(t)\rightarrow y_{2}(t) $
then
$ axi $
