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 H(t).cos(w0t)

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Fourier Transform f(t)=H(t).cos(ω0t) ,using the transform of H(t)

    H(t)=Heaviside function (also known as signal function if I ain't wrong)

    2. Relevant equations

    (1) FT[f(t)] = ∫ f(t).e^-(iωt) dt

    (2) FT[H(t)] = pi.δ(ω) + 1/iω

    (3) δ(ω) = Delta Dirac Function

    (4) FT[cos(ω0t)] = pi (δ(ω-ω0) + δ(ω+ω0))

    3. The attempt at a solution

    I used equation (1) to get it, integrating by parts. The first part of parts integration yealds 0, then the new integral has the derivative of H(t), which is not bad since we can use the derivative propertie of the transform, but integrating cos(ω0t).e^-(iωt) yealds something quite far from the expected result. Am I on the right way? Any suggestions?

    Thank you for any help
  2. jcsd
  3. Feb 6, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Please show the details of your work.
  4. Feb 6, 2012 #3
    I got it! You have to make cos(ω0t) = 1/2 (e^(iω0t) + e^-(iω0t)) (euler formula)

    Then use the linearity propertie of the transform and then the modulation propertie.

    Thanks for such a quick response anyway =)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook