Fourier Transform Question

  • #1

Homework Statement


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.

Homework Equations



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

Thanks in advance

The Attempt at a Solution

 

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Answers and Replies

  • #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].
 
  • #3
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].
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?
 
  • #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.
 
  • #5
Check your signs. One factor will be just j and the other one will be -j, which conveniently flips the sign of that term.
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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