| Line 7: | Line 7: | ||
For any <math>x_{1}(t) \; \rightarrow \; y_{1}(t)</math> and <math>x_{2}(t) \; \rightarrow \; y_{2}(t)</math> | For any <math>x_{1}(t) \; \rightarrow \; y_{1}(t)</math> and <math>x_{2}(t) \; \rightarrow \; y_{2}(t)</math> | ||
| − | \ | + | \indent and any complex constants <math>a</math> and <math>b</math> |
| − | + | ||
| − | + | ||
then | then | ||
<math>ax_{1}(t)+bx_{2}(t)\rightarrow</math> | <math>ax_{1}(t)+bx_{2}(t)\rightarrow</math> | ||
Revision as of 20:06, 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) $
\indent and any complex constants $ a $ and $ b $
then
$ ax_{1}(t)+bx_{2}(t)\rightarrow $
