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?
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1Hint: there is this inverse Fourier transform of a sign-function that helps to connect. – al-Hwarizmi Aug 22 '13 at 14:19