Help finding ths Fourier transform

  • #1

Homework Statement


find the fourier transform of the following function in two ways , once using direct computation , and second using the convolution therom .

Homework Equations


Acos(w0t)/(d2+t2)

The Attempt at a Solution


I tried first to solve directly . used Euler's identity and got
∫e-it(w0+w)/(d2+t2) + ∫eit(w0-w)/(d2+t2)

but I think it was a deadend , unsolvable integral .

I got a hint from an internet source saying to use the Lorentzian transform but I am not familiar with it

then I tried going first from the convolution approach , which means I find the separate F transform of cos(w0t) and of 1/(d2+t2) and then calculate the convolution of them in order to get the FT of the multiplication oh them .

I couldn't do that as well because I didn't manage to integrate e-iwt/(d2+t2) and so can't find that fourier transform as well

any direction ,or explained hint would be greatly appreciated!
 
Last edited:

Answers and Replies

  • #2
phyzguy
Science Advisor
4,746
1,675
This integral can be done using partial fractions, expanding the denominator as (d+t) * (d-t). It then gives a sum of terms of the exponential integral (Ei) function. Or you could just look it up.
 

Related Threads on Help finding ths Fourier transform

Replies
3
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
2
Views
603
Replies
2
Views
1K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
5
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
7
Views
1K
  • Last Post
Replies
1
Views
2K
Top