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authorsiveshs <siveshs@gmail.com>2010-07-03 04:23:48 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-03 04:23:48 +0000
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section 3 editing
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@@ -121,7 +121,7 @@ In order to prove orthonormality of the basis vectors:
$$
\begin{array}{ccl}
-(f_n,f_m) = \int_0^{2\pi} \, \frac{1}{\sqrt{2\pi}} \, e^{inx} \, \longbar {\frac{1}{\sqrt{2\pi}} \, e^{inx}} \, dx\\
+(f_n,f_m) = \int_0^{2\pi} \, \frac{1}{\sqrt{2\pi}} \, e^{inx} \, \bar {\frac{1}{\sqrt{2\pi}} \, e^{inx}} \, dx\\
& = & \frac{1}{2\pi} \, \int_0^{2\pi} \, e^{i(n-m)x} \, dx \\
Here, n = m \Rightarrow (f_n,f_m) & = & 1\\
n \neq m \Rightarrow (f_n,f_m) & = & 0\\