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!

Homework Help: Fourier transform of cos(100t)

  1. Aug 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the fourier transform of cos(100t)

    3. The attempt at a solution
    now I know just from looking at a fourier transform table that if the equation is in the form cos(2Pi*k*t) then the answer is just 1/2(delta(f+k) + delta(f-k))

    So in this case is the answer 1/2(delta(f+100/2pi) + delta(f - 100/2pi)) ?

    I'm not that good at integrals so I haven't attempted to do this problem the traditional long way.

    Thanks :)
  2. jcsd
  3. Aug 13, 2009 #2


    User Avatar
    Homework Helper
    Gold Member

    Write out the Fourier transform integral, and write cos(100t) as a sum of exponentials using Euler's formula. Then use the following fact:

    [tex] \frac{1}{2\pi} \int_{-\infty}^{\infty} e^{ixy} dy = \delta(x) [/tex]
  4. Aug 13, 2009 #3
    Ok starting with S e^(-2Pi*i*t) * (e^(i100/2pi*t) + e^(-i100/2pi*t))/2

    I got it down to 1/2PI S (e ^(-2Pi*i(t + 100/2Pi) + e ^ (-2Pi*i(t - 100/2pi))

    Which then equals delta(f + 100/2Pi) + delta (f - 100/2pi)

    I'm not sure if I did it correctly though or just worked my way backwards from the answer (I attempted this originally and then got stuck). Does that look like I am going in the right direction?
  5. Aug 13, 2009 #4


    User Avatar
    Homework Helper
    Gold Member

    cos(100t) = (ei100t + e-i100t)/2

    I don't understand where you got the 2pi's in it.
  6. Aug 13, 2009 #5
    I did that originally so I could use the transform table, its ok I understand what to do now. I will have a shot at doing it from scratch and report back.

    Thanks guys.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook