TT2--Problem 4

[Victor Ivrii]

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

Post after 22:30

[Ian Kivlichan]

Hopeful solution attached!

[Victor Ivrii]

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 $\int_0^\infty \frac{1-\cos(\omega)}{\omega^2}\,d\omega$.