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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^{- | + | FS Coefficients: <math>a_ke^{-jkw_0t_0}</math> |
| Line 10: | Line 10: | ||
If we plug the new FS Coefficients into the CTFS function,we get: | If we plug the new FS Coefficients into the CTFS function,we get: | ||
| − | <math>\sum_{k=-\infty}^\infty a_ke^{- | + | <math>\sum_{k=-\infty}^\infty a_ke^{-jkw_0t_0}e^{jkw_0t}</math> = <math>\sum_{k=-\infty}^\infty a_ke^{jkw_0(t-t_0)}</math> = <math>x(t-t_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) $
