# Fourier Transform Question

1. Sep 10, 2011

### frenzal_dude

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.

3. The attempt at a solution

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• ###### question1.jpg
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2. Sep 12, 2011

### vela

Staff Emeritus
Multiply the exponential factor through and use the fact that $\delta(f-f_0) h(f) = \delta(f-f_0) h(f_0)$.

3. Sep 12, 2011

### frenzal_dude

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. Sep 12, 2011

### vela

Staff Emeritus
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. Sep 12, 2011

### frenzal_dude

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!