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 sin(t)/t

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Evaluate INT(|X(t)|^2) dt using parsevals theorem

    where x(t) = (sin(t)cos(10t))/(pi*t)

    2. Relevant equations

    parsevals theorem: int(|f(t)|^2 dt = (1/2*pi)INT(|F(W)|^2 dw

    3. The attempt at a solution

    So I've tried several attempts at this problem and this is my latest:

    first I use the fact that sin(x)*cos(y) = (sin(x+y)+sin(x-y)) /2
    to get sin(t)cos(10t)/pi*t = (sin(t+10t) + sin(t - 10t))/(2*pi*t)

    then I split it up into : sin(11t)/2t*pi + sin(-9t)/2t*pi

    then what I was going to do was take the fourier transform of each function here however, I can't figure out how in the world to take the fourier transform of sin(t)/t

    anyone have any ideas? thanks!
  2. jcsd
  3. Oct 4, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Do you know a function whose Fourier transform is [itex]\sin(\omega)/\omega[/itex]?
  4. Oct 4, 2009 #3
    I checked on my transform table and looked around online a little and didn't see any transform that equals sin(w)/w. If there was i'd use the f(w) <-> F(t) rule and then it could work for me. Does that transform exist?
  5. Oct 4, 2009 #4

    Compute the (inverse) Fourier transform of f(x), defined as:

    f(x) = 1 for -L < x < L,

    otherwise f(x) = 0
  6. Oct 4, 2009 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, it exists and is one of the most fundamental transforms! If your table doesn't have it, I would get another table (seriously). Count Iblis' hint is right on the money.

    By the way, [itex]\sin(x)/x[/itex] is sometimes called [itex]sinc(x)[/itex], so look in your table for that. Caution: some authors define [itex]sinc(x) = \sin(\pi x)/(\pi x)[/itex].
    Last edited: Oct 4, 2009
  7. Oct 4, 2009 #6
    ooohhhh now it makes sense!!! thank you!! XD
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Fourier transform of sin(t)/t
  1. Fourier Transform of 1/t (Replies: 15)