1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to take the fourier transform of a function?

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the fourier transform of x(t) = e-t sin(t), t >=0.

    We're barely 3 weeks into my signals course, and my professor has already introduced the fourier transform. I barely understand what it means, but I just want to get through this problem set.


    2. Relevant equations
    I honestly don't know. I know it's an improper integral with bounds -∞ and ∞, that is
    ∫x(t)e-j2∏tdt


    3. The attempt at a solution
    I get something VERY LONG which does not seem right.
     
    Last edited: Sep 17, 2012
  2. jcsd
  3. Sep 17, 2012 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    How can sin(t) expressed in exponential notation?

    BTW your integral is missing dt. It is dt, right?
     
  4. Sep 17, 2012 #3
    Yes, that is correct.

    I know that sin(t) = (1/2) * j * (e-t - et), so x(t) = (1/2)*j*(et(-j-1) - et(j-1)). But then I'd have something really painful to integrate, right?
     
  5. Sep 17, 2012 #4

    rude man

    User Avatar
    Homework Helper
    Gold Member

    You're right, can't do it that way. Will come back to you in a short while.
     
  6. Sep 17, 2012 #5

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Looks like convolution in the frequency domain is the way to go. You remember the convolution theorem?

    So you'll need F(ω) for f(t) = exp(-at) and f(t) = sin(ωt), both for t > 0 and both = 0 for t < 0. The first one is easy; let me know how you're managing with the second ... remember when you take F(ω) to integrate from 0 to ∞, not -∞ to +∞.

    EDIT: never mind convolution. You can do the integral.

    The integral is not as bad as you think. Key point is that lim t→∞ {e-(a + jb)t} = 0 providing a > 0 which it is in your case.
     
    Last edited: Sep 17, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to take the fourier transform of a function?
  1. Fourier Transform (Replies: 2)

  2. Fourier Transforms (Replies: 5)

Loading...