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We know that: | We know that: | ||
| − | <math>x(t)=cos(2t)=\frac{e^{2jt}+e^{-2jt}{2}</math> | + | <math>x(t) = cos(2t)= \frac{e^{2jt}+e^{-2jt}{2}</math> |
Revision as of 09:18, 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) $
We know that: $ x(t) = cos(2t)= \frac{e^{2jt}+e^{-2jt}{2} $
