# Inverse Fourier transform of $f|X(f)|$

The inverse Fourier transform of $fX(f)$ is simply given by

$$\frac{1}{j2\pi}\frac{dx(t)}{dt}$$.

But what is the inverse Fourier transform of the following term?

$$f|X(f)|$$

Does the inverse Fourier transform exist?

• Hint: there is this inverse Fourier transform of a sign-function that helps to connect. – al-Hwarizmi Aug 22 '13 at 14:19