I need to find the fourier transform of f(x)=(1-abs(x))(Chi_[-1,1] (x)). In words, I need the fourier transform of one minus the absolute value of x multiplied by the characteristic function on interval -1,1.
I tried using the convolution theorem and finding the fourier transform for both functions separately, but then I realized I didn't understand how to compute the convolution of the separate transforms. Can someone please explain how I would go about finding this transform?
I got an answer of -1/ξ^2 (2isin(ξ) but I am not sure if this correct. I am using the fourier definition of:
(1/2pi) integral of f(x)e^(-iξx) dx