| Line 1: | Line 1: | ||
Proof of Time Shifting in CTFS(Table 3.1) | Proof of Time Shifting in CTFS(Table 3.1) | ||
| − | Peridic Signal: x(t- | + | Peridic Signal: <math>x(t-t_0)</math> |
FS Coefficients: <math>a_ke^{-jkw_0t_0}</math> | FS Coefficients: <math>a_ke^{-jkw_0t_0}</math> | ||
Latest revision as of 18:35, 8 July 2009
Proof of Time Shifting in CTFS(Table 3.1)
Peridic Signal: $ x(t-t_0) $
FS Coefficients: $ a_ke^{-jkw_0t_0} $
Proof:
If we plug the new FS Coefficients into the CTFS function,we get:
$ \sum_{k=-\infty}^\infty a_ke^{-jkw_0t_0}e^{jkw_0t} $ = $ \sum_{k=-\infty}^\infty a_ke^{jkw_0(t-t_0)} $ = $ x(t-t_0) $
