10/09 - Fourier Transform

Fourier Transform

$\left\langle e^{j2\pi nt/T}\mid e^{j2\pi mt/T}\right\rangle$	$=\int _{-\infty }^{\infty }e^{j2\pi nt/T}e^{-j2\pi mt/T}\,dt$
	$=\int _{-\infty }^{\infty }e^{j2\pi (n-m)t/T}\,dt$

• This is undefined due to the limits. The notes say that the integral = T, but no limits were defined. How would you know to do -T/2 to T/2?