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: Help with fourier transform for special square wave

  1. Oct 21, 2009 #1
    I know how to describe a square wave with fourier analysis, but what if I'm looking for a square wave with "peaks" that are longer than the "valleys."
    For example, from f(x)=1 {from 0 to 2}, f(x)=-1 {from 2 to 3}, f(x)=1 {from 3 to 5}, f(x)=-1 {from 5 to 6}.... and so on in a periodic fashion.
    Any ideas?
  2. jcsd
  3. Oct 21, 2009 #2

    Andy Resnick

    User Avatar
    Science Advisor
    Education Advisor

    That's not so bad- first, I'll rectify the wave and re-normalize it to make the functions easier to type.

    Then, the wavetrain you describe is rect(x/2)*comb(x/4), where '*' is convolution. I'm pretty sure that will reproduce the function you describe. The Fourier transform is then Sinc(2q)*Sinc(4q), where sinc(x) = sin(x)/x, and q is the conjugate variable to x.

    Tweak the original function as needed.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook