| Line 5: | Line 5: | ||
So <math> x(t) = e^{j2\pi t} </math> for <math> |t| < 3 \,</math><br><br> | So <math> x(t) = e^{j2\pi t} </math> for <math> |t| < 3 \,</math><br><br> | ||
| − | And <math> x(t) = 0 </math> for otherwise | + | And <math> x(t) = 0 \,</math> for otherwise |
Revision as of 17:51, 7 October 2008
$ X(w) = \frac{2sin{3(w-2\pi)}}{w-2\pi}\, $
We already knew that when $ x(t) = \frac{sinWt}{\pi t}, X(w) = 1 for |w|<W. \, $
when$ x(t) = x(t-t_0), X(w) = e^{-jwt_0}X(jw) $
W is 3 , and this was delayed $ 2\pi\, $
So $ x(t) = e^{j2\pi t} $ for $ |t| < 3 \, $
And $ x(t) = 0 \, $ for otherwise
