HW3.B Hetong Li ECE301Fall2008mboutin - Rhea

System Response

Based on the Euler Formula, $ \cos(2t)\,= \frac{e^{2jt}+e^{-2jt}}{2}\, $.

We already had the response of $ e^{2jt}\, $ is $ te^{-2jt}\, $ and the response of $ e^{-2jt}\, $ is $ te^{2jt}\, $.

Since the system is a LTI system, we have

Output = Response($ \frac{e^{2jt}+e^{-2jt}}{2}\, $)

      = Response($ \frac{e^{2jt} $)+

     $ =\frac{te^{2jt}+te^{-2jt}}{2}\, $

     $ =t\frac{e^{2jt}+e^{-2jt}}{2}\, $

     $ =t\cos(2t)\, $