| 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^{-jkw0t0}e^{jkw0t}</math> = <math>\sum_{k=-\infty}^\infty a_ke^{jkw0(t-t0}</math> | + | <math>\sum_{k=-\infty}^\infty a_ke^{-jkw0t0}e^{jkw0t}</math> = <math>\sum_{k=-\infty}^\infty a_ke^{jkw0(t-t0)}</math> = x(t-t0) |
Revision as of 18:32, 8 July 2009
Proof of Time Shifting in CTFS(Table 3.1)
Peridic Signal: x(t-t0)
FS Coefficients: ak*exp(-jkw0t0)
Proof:
If we plug the new FS Coefficients into the CTFS function,we get:
$ \sum_{k=-\infty}^\infty a_ke^{-jkw0t0}e^{jkw0t} $ = $ \sum_{k=-\infty}^\infty a_ke^{jkw0(t-t0)} $ = x(t-t0)
