| Line 12: | Line 12: | ||
then | then | ||
| − | <math>ax_{1}(t)+bx_{2}(t)\rightarrow</math> | + | |
| + | <math>ax_{1}(t) \; +bx_{2}(t) \; \rightarrow \; ay_{1}(t) \; + by_{2}(t)</math> | ||
Revision as of 20:08, 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 \; ay_{1}(t) \; + by_{2}(t) $
