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anonymous
 4 years ago
find the fourier transform of the following function:
\[f(x)=x , 1\leq x \leq 1, f(x) = 0 \abs{x} \geq 1\]
anonymous
 4 years ago
find the fourier transform of the following function: \[f(x)=x , 1\leq x \leq 1, f(x) = 0 \abs{x} \geq 1\]

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ah, that \abs is supposed to be the absolute value encompassing x

nikvist
 4 years ago
Best ResponseYou've already chosen the best response.0\[F(\omega)=\int\limits_{\infty}^{+\infty}f(x)e^{i\omega x}dx=\int\limits_{1}^{1}xe^{i\omega x}dx=\]\[=\int\limits_{1}^{1}x(\cos{\omega x}i\sin{\omega x})dx=\]\[=\underbrace{\int\limits_{1}^{1}x\cos{\omega x}dx}_{=0}i\int\limits_{1}^{1}x\sin{\omega x}dx=2i\int\limits_{0}^{1}x\sin{\omega x}dx=\]\[=2i\frac{\sin{\omega}\omega\cos{\omega}}{\omega^2}\]
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