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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} $

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Sean Hu, ECE PhD 2009