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) $

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