| Line 3: | Line 3: | ||
when<math> x(t) = x(t-t_0), X(w) = e^{-jwt_0}X(jw)</math><br><br> | when<math> x(t) = x(t-t_0), X(w) = e^{-jwt_0}X(jw)</math><br><br> | ||
W is 3 , and this was delayed <math>2\pi\,</math><br><br> | W is 3 , and this was delayed <math>2\pi\,</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 </math> | ||
Revision as of 18:51, 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 </math>
