Toronto Math Forum
APM3462012 => APM346 Math => Term Test 2 => Topic started by: Victor Ivrii on November 15, 2012, 08:23:51 PM

Find Fourier transform of the function
\begin{equation*}
f(x)= \left\{\begin{aligned}
&1x &&x<1\\
&0 &&x>1.
\end{aligned}\right.
\end{equation*}
and write this function $f(x)$ as a Fourier integral.
Post after 22:30

Hopeful solution attached! :)

Actually since $f$ is an even function so is $\hat{f}$ and $f(x)$ could be written as $\cos$Fourier integral.
BTW plugging $x=0$ we can calculate $\int_0^\infty \frac{1\cos(\omega)}{\omega^2}\,d\omega$.