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Transfer function from amplitude response?

  1. Apr 23, 2010 #1
    Hi, in the paper I've attached, they give a method for generating a polynomial g for the amplitude response of a filter that gives arbitrary flatness and roll-off characteristics.

    [tex]\frac{1}{\sqrt{1+g}}[/tex]

    And then they say the transfer function can be easily determined from this, but they don't say how.

    For example, they give an amplitude response

    [tex]\frac{1}{\sqrt{1+10s^{8}-24w^{10}+15w^{12}}}[/tex]

    and then they just say "then we will have the transfer function"

    [tex]\frac{0.259}{s^{6}+2.392w^{5}+3.661s^{4}+2.755s^{3}+2.615s^{2}+1.162s+0.259}[/tex]

    I know how to get the transfer function from the amplitude response for a standard filter like a butterworth or chebyshev, but for ones like this?
     

    Attached Files:

  2. jcsd
  3. Apr 27, 2010 #2
    Hey, I figured it out. I wrote a Mathematica note book that does it. Anyone want it?
     
  4. Apr 27, 2010 #3

    berkeman

    User Avatar

    Staff: Mentor

    Cool. Yes please, it would be fun to try out. Can you post it as an attachment?
     
  5. May 2, 2010 #4
    Yeah.
     

    Attached Files:

    • p1_3.nb
      p1_3.nb
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