- #1

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**The attempt at a solution**

Clearly everything is simple if you know X(f), because y(t)=InverseFourier{ X(f)

^{2}}. The problem is that I can't find X(f). By the way, because x(t) is even, I can use the easier version of the transform, but it doesn't help so much, in the end I have to solve:

I tried in vain with some trigonometric formula, but I still have product of sin/cos in the end.

Trying with the convolution product doesn't help either, because I get this:

And I can't see anything that may help me...

Wolfram says this is the solution:

EDIT: wait a minute! I'm dumb! because I can use the modulation theorem.....1/4 sqrt(pi/2) (sgn(-w-20pi+1)+sgn(-w+20pi+1)+sgn(w-20pi+1)+sgn(w+20pi+1))