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[Fourier transform] Convolution product with sin and cos

  1. Nov 27, 2014 #1
    I'm asked to transform y(t) = x(t)*x(t) (where * is the convolution product) and x(t)= sinc(t)cos(2π10t) ( sinc(t)= sin(πt)/(πt) ).


    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:
    W4RJlCC.jpg
    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:
    iRsJv0m.jpg
    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.....
     
  2. jcsd
  3. Nov 27, 2014 #2
    You may put all of this stuff into the exponential form.. :)
     
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