Basics of Linearity
Given:
$ e^{2jt}\! $ through a system produces $ e^{-2jt}\! $, and $ e^{-2jt}\! $ produces $ e^{2jt}\! $. what is the output of $ cos(2t)\! $
Answer:
$ cos(2t)\! $ can also be written as $ (e^{2jt} + e^{-2jt})/2\! $ which can also be written as $ 1/2*[(e^{2jt} + e^{-2jt})]\! $ so therefore the linear system's response is $ t/2*[(e^{-2jt} + e^{2jt})]\! $ which equals $ t/2*cos(2t)\! $.
(Note: The star in this case is the multiplication operator, not the convolution operator)
