ASN3 - Class Notes October 5

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$1/T⟶df$

$n/T⟶f$

$\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}\frac{1}{T}⟶\underset{-\mathrm{\infty }{]}^{\mathrm{\infty }}}{\int }()df$

THE GAME

LTI (Linear Time Invariant System) Input LTI Output Reason

$x2(t)$ . $e^{\frac{-j2\pi mt}{T}}=\underset{-\frac{T}{2}}{\overset{\frac{T}{2}}{\int }}\sum _{n=0}^{\mathrm{\infty }}{a}_n{e}^{\frac{j2\pi nt}{T}}{e}^{\frac{-j2\pi mt}{T}}dt=\sum _{n=0}^{\mathrm{\infty }}{a}_n\underset{-\frac{T}{2}}{\overset{\frac{T}{2}}{\int }}{e}^{\frac{j2\pi (n-m)t}{T}}dt=\sum _{n=0}^{\mathrm{\infty }}{a}_{n}T{\delta }_{mn}$