Inverse Fourier transforms and partial fractions

[Luongo]

1. find the inverse FT of 1/(iw+3)³



2. well partial fractions gave the same thing back... I'm not sure how to transform this as there's no property that deals with cubics.



3. i tried using the differentiation property but it doesn't work as it increases the power of 3 to 4 and so on... how would i go about computing the inverse Fourier transform of this? is there a property involving powers out there? how would you

 

[HallsofIvy]

I'm not familiar with using partial fractions for inverse Fourier transforms but it looks like that would be easy to integrate directly. Do you mean Laplace transform?

 

[Luongo]

I'm not familiar with using partial fractions for inverse Fourier transforms but it looks like that would be easy to integrate directly. Do you mean Laplace transform?

the course is called "the Fourier transform and its applications" so yeah I'm pretty sure i don't mean laplace transform. can someone help please my midterms tommorow and i have no clue..

 

[Dingledorf]

Hey Luongo, did you ever figure out how to do this problem? I have the exact same question on my problem set and have no idea what to do either, I ended up trying partial fractions just like you and it didn't work so I'm stumped.

 

[SammyS]

1/(iw+3) = 3/(w² +9) - iw/(w² +9) = (1/√(w² +9))e^{i arctan(w/3)}