1. Limited time only! Sign up for a free 30min personal 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!

Fourier Transform of exponential and heaviside function

  1. Aug 29, 2011 #1
    1. The problem statement, all variables and given/known data
    Compute the Fourier transform of

    [itex]\phi(t)[/itex]=(e^(-at))H(t)

    where H(t) is the Heaviside step function


    2. Relevant equations



    3. The attempt at a solution
    I am stuck in an attempt at the solution, I am confused at how the heaviside step function factors in and think that it may just affect the upper and lower limits of the integral, but am not sure. I am looking for direction on how to approach the problem or at least set it up.
     
  2. jcsd
  3. Aug 29, 2011 #2

    Char. Limit

    User Avatar
    Gold Member

    The Fourier Transform is defined on a function f(t) as:

    [tex]\int_{-\infty}^\infty f(t) e^{2 \pi i t \omega} dt[/tex]

    Now, try plugging in f(t)=e^(-at)H(t) into this definition. Remember that H(t) is defined to be 0 for all negative t and 1 for all positive t, so try splitting the integral into two integrals: one with lower bound -infinity and upper bound 0, and the other with lower bound 0 and the upper bound infinity. Then apply the definition of H(t) and it should become easy.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fourier Transform of exponential and heaviside function
Loading...