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

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