Let $f=\begin{cases}1-x^2,\:{x}\leq1\\x-1,\:x>1\\-x-1,\:x<-1\end{cases}$ (at the picture below). Find Fourier transform $Ff$.
I am hopelessly stuck, completely out of ideas.
- I've tried to operate by the definition but the calculations were too cumbersome.
- I've taken a first derivative but could not find a constant.
- I've taken a second derivative, too, but could not find one of two constants.
Could you please help me?
