| Line 16: | Line 16: | ||
From Euler's formula | From Euler's formula | ||
| − | <math>e^{iy}=cos{y}+ | + | <math>e^{iy}=cos{y}+i sin{y}</math> |
| + | |||
| + | We know that: | ||
| + | x(t) = cos(2t)= <math>\frac{e^{2jt}+e^{-2jt}}{2}</math> | ||
Revision as of 11:46, 18 September 2008
As discussed in class,a system is called linear if for any constants a,b belongs to phi and for anputs x1(t), x2(t) (x1[n],x2[n]) yielding output y1(t) , y2(t) respectively the response to
ax1(t) + bx2(t) is ay1(t)+by2(t).
Consider the following system: $ e^{2jt}\to system\to te^{-2jt} $
$ e^{-2jt}\to system\to te^{2jt} $
From the given system:
$ x(t)\to system\to tx(-t) $
From Euler's formula $ e^{iy}=cos{y}+i sin{y} $
We know that: x(t) = cos(2t)= $ \frac{e^{2jt}+e^{-2jt}}{2} $
