How to Solve Inverse Fourier Transform of (10*sin(3*omega)) / (omega+Pi)?

[bangell]

Can someone help me and tell me the steps to solve the inverse Fourier transform of the following function

(10*sin(3*omega)) / (omega+Pi)


Thanks!

 

[ledol83]

You will need to integrate "this function times exp(i*omega*t)" over omega from -inf to +inf. The resulting thing is a function of t, which is in the time domain, as usually called.

 

[bangell]

How would I work this out by hand? I know you probably need to use trig identities in order to simplify the problem. Do you have any suggestions.

 

[ledol83]

you know exp(iwt)=cos(wt)+i*sin(wt); then you're right, triangle idents are needed. Just treat i as a constant, and it won't hurt other calculation.

 

[bangell]

I'm still just confused of how to get a simplified answer. Do you have time to work the problem out and let me know what sort of answer you get?

Thanks for all your help.