convert elliptic transfer coefficients to polynomial

Hi,

I'm trying to convert an elliptic transfer function where i have
knowledge of the poles and zeros (transmission and reflection) into the
s-coefficients.

is there a matlab routine in which i can do this?

my data is this:

========= Prototype Pole-Zero Data =========
                   (a + jb)
      S21 Poles          S21 Zeros     S11 Zeros
-0.1805      0.89515      0  2.02         0  0
-0.015829    1.013        0  1.308        0  0.99523
-0.065342    0.9861       0  1.125        0  0.94958
-0.40772     0.61869      0  1.074        0  0.81465
-0.57956     1.8358e-016  0  -2.02        0  0.5058
-0.40772     -0.61869     0  -1.308       0  -0.99523
-0.1805      -0.89515     0  -1.125       0  -0.94958
-0.015829    -1.013       0  -1.074       0  -0.81465
-0.065342    -0.9861      0  0            0  -0.5058    

regards,

Phil

Phil Newman wrote:
> Hi,
>
> I'm trying to convert an elliptic transfer function where i have
> knowledge of the poles and zeros (transmission and reflection) into the
> s-coefficients.
>
> is there a matlab routine in which i can do this?
>
> my data is this:
>
> ========= Prototype Pole-Zero Data =========
>                    (a + jb)
>       S21 Poles          S21 Zeros     S11 Zeros
> -0.1805      0.89515      0  2.02         0  0
> -0.015829    1.013        0  1.308        0  0.99523
> -0.065342    0.9861       0  1.125        0  0.94958
> -0.40772     0.61869      0  1.074        0  0.81465
> -0.57956     1.8358e-016  0  -2.02        0  0.5058
> -0.40772     -0.61869     0  -1.308       0  -0.99523
> -0.1805      -0.89515     0  -1.125       0  -0.94958
> -0.015829    -1.013       0  -1.074       0  -0.81465
> -0.065342    -0.9861      0  0            0  -0.5058
>
> regards,
>
> Phil

Hello Phil,

Just multiply them out. For example:

(s-(-0.1805+j0.89515))(s-(-0.1805-j0.89515)

If you use your roots in conjugate pairs, the resulting polys are real
valued.


(s-a-jb)(s-a+jb) = s^2 -2as + a^2 + b^2

You will likely want to have your result as a few biquads. So using
conjugate pairs for the poles and zeroes, you generate a handful of
quadratic real terms. Then pair up a zero term with a pole term to form
a biquad.


IHTH,

Clay