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Homework Help: Inverse fourior transform?

  1. Nov 9, 2006 #1
    How do I find inverse fourier transform of 1/(1+8e^3jw)??
    Now, it would have been easier to find inverse of 1/(1+1/8e^jw), because that would be just (1/8)^n u[n]
    i think i basically need a way to write 1/(1+8e^3jw) in a form described below:
    A/(1+ae^(jw)) + B/(1+be^(jw) +C/(1+ce^(jw)
    where a, b, c are less than 1.
    How do I do that? partial fraction can be killing, because the process will be too long. Any other smarter methods?
  2. jcsd
  3. Dec 20, 2011 #2
    find (2-e^(-jw))/(1+e^(-j3w)/8) inverse fourier transform
  4. Dec 20, 2011 #3
    How about just muscle-through the contour integration:

    [tex]\frac{1}{2\pi i}\int_{-\infty}^{\infty} \frac{e^{iwx}}{1+8e^{3iw}}dw[/tex]

    I suspect that may be just a sum of residues if x>0 however I've not gone over it rigorously so I'm not sure. Just another possibility you may wish to consider.
    Last edited: Dec 20, 2011
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