Have you ever seen a diffraction pattern caused by any discontinuities?
I have seen thousands of them ... the fourier transform of any discrete functions makes very nice detectable pattern that says : "NOT NATURAL". And that what radars are trained for spotting.
And the more symmetries the more the pattern reinforce itself saying: human made technology spotted. (Curie principle : symmetry in causes get propagated in the effects)
Have you seen a lot of natural object that are both discontinuous and symmetric and the size of a plane?
EDIT : I forgot to explain the relationship between convolution of signals and FT but I guess everyone is educated enough to know that convolution of signal is the base of radar detection and that Fourier transform are related to convolution.