10/09 - Fourier Transform: Difference between revisions

Revision as of 13:53, 17 November 2008

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

This is undefined due to the limits. The notes say that the integral = T, but no limits were defined. You would only know to do -T/2 to T/2 if you knew the function was periodic with period T.

@@ Line 7: / Line 7: @@
 |<math>=\int_{-\infty}^{\infty}e^{j2\pi (n-m) t/T}\,dt</math>
 |}
-*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?
+*This is undefined due to the limits. The notes say that the integral = T, but no limits were defined. You would only know to do -T/2 to T/2 if you knew the function was periodic with period T.
 ==Fourier Transform==