10/09 - Fourier Transform: Difference between revisions

Revision as of 13:53, 17 November 2008

$⟨ e^{j 2 π n t / T} ∣ e^{j 2 π m t / T} ⟩$	$= \int_{- \infty}^{\infty} e^{j 2 π n t / T} e^{- j 2 π m t / T} d t$
	$= \int_{- \infty}^{\infty} e^{j 2 π (n - m) t / T} d t$

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==