2
$\begingroup$

I've come to realize that the Fourier transform of an already Fourier transformed signal gives the time-reversal signal.

$$\mathcal F(\mathcal F(x(t)))=x(−t)$$

ref 1,ref 2

However, my question is, if Fourier transformation is applied to the magnitude of the Fourier transformed signal (excluding phase information), is there a way to interpret the returned signal?

$$\mathcal F\{|\mathcal F\{x\}|\}=?$$

$\endgroup$
6
$\begingroup$

If it were the squared magnitude, the result would be the auto-correlation function, apart from a time inversion and possibly a scaling factor. If it's just the magnitude, then the result can be characterized as the only even function that has the same Fourier transform magnitude as the original function.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.