HW3.B Jun Hyeong Park ECE301Fall2008mboutin - Rhea

• I am going to use the definition of Linearity that I learned in class.
• The definition
  

 if x1(t) --> system --> y1(t)

    x2(t) --> system --> y2(t)

 Then ax1(t) + bx2(t) --> system --> ay1(t) + by2(t) , for any complex constants a,b 

$ e^{(2jt)} = cos{(2t)} + jsin{(2t)} --> system --> t*{(cos{(2t)} - jsin{(2t)})}\, $
$ e^{(-2jt)} = cos{(2t)} - jsin{(2t)} --> system --> t*{(cos{(2t)} + jsin{(2t)})}\, $

Now, suppose a and b are 1/2.
$ \frac{1}{2}e^{(2jt)} + \frac{1}{2}e^{(-2jt)} = \frac{1}{2}(cos{(2t)} + jsin{(2t)}) + \frac{1}{2}(cos{(2t)} - jsin{(2t)}) = cos{(2t)} $