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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?
    Thanks
     
  2. jcsd
  3. Oct 21, 2009 #2

    Andy Resnick

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    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.
     
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