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Fourier Transform Question

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Hi, I tried to work out the FT of cos(theta), and sin(theta + pi/2) which should both give the exact same FT since they are the same function.

    However I get two different results as shown in the .jpg.

    2. Relevant equations

    I used the 'time shifting' property to get that exponential in the second part.

    Thanks in advance

    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Sep 12, 2011 #2

    vela

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    Multiply the exponential factor through and use the fact that [itex]\delta(f-f_0) h(f) = \delta(f-f_0) h(f_0)[/itex].
     
  4. Sep 12, 2011 #3
    Thanks for your help! I never realised that.

    I managed to work it out to almost the same as the cos function FT, however I am still left with the minus sign before the 2nd delta function, how do you get rid of that?
     
  5. Sep 12, 2011 #4

    vela

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    Check your signs. One factor will be just j and the other one will be -j, which conveniently flips the sign of that term.
     
  6. Sep 12, 2011 #5
    Yes you are right. I forgot to sub in f=-f0 for the 2nd exponential.

    It works out perfectly.

    Thanks a lot for your help!
     
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