| Line 5: | Line 5: | ||
If the system is linear, then the following is true: | If the system is linear, then the following is true: | ||
| − | For <math>x_{1}(t)\rightarrow y_{1}(t)</math> | + | For any <math>x_{1}(t) \; \rightarrow \; y_{1}(t)</math> and <math>x_{2}(t)\rightarrow y_{2}(t)</math> |
| − | and <math> | + | and any complex constants <math>a</math> and <math>b</math> |
then | then | ||
| − | <math> | + | <math>ax_{1}(t)+bx_{2}(t)\rightarrow</math> |
Revision as of 20:59, 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 any $ x_{1}(t) \; \rightarrow \; y_{1}(t) $ and $ x_{2}(t)\rightarrow y_{2}(t) $
and any complex constants $ a $ and $ b $
then
$ ax_{1}(t)+bx_{2}(t)\rightarrow $
