Fourier Transform question F o sin(10t)

[priscared]

Fourier Transform of sin(10t)

Hi all,
Can some1 explain how to get the complex Fourier transform of sin(10t)

I understand how to steal it off a Fourier transform table, but i have no idea how to do it manually.

Any help anyone?
Cheers

 

[daviddoria]

The Fourier transform of a pure tone (the sine function) is two delta function, one at $$+\frac{10}{2\pi}$$ and the other at $$-\frac{10}{2\pi}$$ (I could have my $${2\pi}$$'s wrong). The last part of this question should be a simple sampling in the frequency domain of the transform of the function in part A.

 

[priscared]

thanks for your reply.
yeah i was way off. Thanks for the clarification

 

[priscared]

Hi,
When answering question above, you stated the need "The last part of this question should be a simple sampling in the frequency domain of the transform of the function in part A."

I believe i have the right rule attached.

e^(j 2pi fc t)g(t) <-> G(f-fc) (this formula is attached in jpeg)

So, once i find the Fourier transform of the first function. I simply need to shift it by fc.

I have had a go at it, i think its right. (answer attached)

If you could point me in the right direction, that'd be great. cheers