Fourier transform of sin

1. May 3, 2009

asi123

1. The problem statement, all variables and given/known data

Hey guys.
I need to find the Fourier transform of sin, is this right?

http://img156.imageshack.us/img156/5531/scan0004r.jpg [Broken]

I searched the internet but all I could find is the answer with the dirac delta and I don't need that.

Thanks.

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. May 3, 2009

dx

The Fourier transform of sin(t) involves the Dirac delta function. What do you mean by "I don't need that"? And why did you change the limits from -∞ to ∞ to -π to π in your integral?

3. May 3, 2009

asi123

Oh, sorry, I need to find it from -pi to pi.
Is there something wrong with what I did?

Thanks.

4. May 3, 2009

dx

I didn't read your whole solution, but there is a mistake in your first step. The Fourier transform integral goes from -∞ to ∞. Why did you change those limits?

5. May 3, 2009

asi123

Yeah, I need to find it from -pi to pi.
Is that way it doesn't involves Dirac function?

Thanks.

6. May 3, 2009

dx

No! It's not from -pi to pi. It's -∞ to ∞.

7. May 3, 2009

asi123

But that is the question.
Find Fourier transform of sin in -pi<t<pi.

What do you mean?

Thanks.

8. May 3, 2009

Cyosis

Your question is to transform the function $$f(t) = \left\{ \begin{matrix} \sin t & \mathrm{if}\; -\pi < t < \pi \\ 0 & \mathrm{otherwise} \end{matrix} \right$$ ?

9. May 3, 2009

asi123

Yeah, sorry for the misconfusion.

10. May 3, 2009

Cyosis

Then your approach is correct since the function is zero outside -pi<t<pi anyway so you may as well integrate from -pi to pi.

11. May 3, 2009

dx

Ah, now it makes sense! Thanks Cyosis!

12. May 3, 2009

Cyosis

You're welcome.