This question is interesting. If you have two signals where one is an image of the other at the symmetry plane f=0 and one image is centered at -f and the other is centered at +f . Assuming that both signals are symmetrical around there center frequencies -f and f which means that every signal has an upper sideband and a lower sideband which are symmetrical. So, under this assumption the upper sideband and the lower side banda are overlapped. Is this description okay. When i get an answer from you then i will continue my answer in the next post depending on you answer.

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Is the signal power or amplitudes?Is x1 symmetrical around the frequency -f and X2 symmetrical around f?You need only to show this symmetry to extend the plot to left of -f and to the right of = +f. Then you can make use full of this symmetry to find out the distortion.

You have also to define the term distortion? What is the overlap interval?

Then the signal will be distorted only in the overlap distortion interval,

so the distorted signal can be expressed by for example

X1 distorted= X1(f) + X2i(f) where X2i(f) is the image of X2 in the overlap frequency interval.

Best wishes