Transfer function from amplitude response?

[cuallito]

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.

$$\frac{1}{\sqrt{1+g}}$$

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

$$\frac{1}{\sqrt{1+10s^{8}-24w^{10}+15w^{12}}}$$

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

$$\frac{0.259}{s^{6}+2.392w^{5}+3.661s^{4}+2.755s^{3}+2.615s^{2}+1.162s+0.259}$$

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?

 

[cuallito]

Hey, I figured it out. I wrote a Mathematica note book that does it. Anyone want it?

 

[berkeman]

Hey, I figured it out. I wrote a Mathematica note book that does it. Anyone want it?

Cool. Yes please, it would be fun to try out. Can you post it as an attachment?

 

[cuallito]

Yeah.