[PD] from poles/zeros to biquad coefficients - how to? (something like max's z-plane)

Funs Seelen funsseelen at gmail.com
Tue Sep 24 15:18:35 CEST 2013

```On Tue, Sep 24, 2013 at 3:08 PM, Funs Seelen <funsseelen at gmail.com> wrote:

> On Tue, Sep 24, 2013 at 2:50 PM, Alexandre Torres Porres <porres at gmail.com
> > wrote:
>
>> one doubt emerges really soon anyway. Since they are complex (there are
>> two coordinate numbers for each pole and zero) how do I get only one number
>> by, for example, summing or multiplying one pole to the other? as in:
>>
>> *b1* = -(P0 + P1)
>> *b2* = (P0*P1)
>>
>
> You don't, the coefficients can be complex too. However, I discovered that
> mirroring (*) every pole and zero results in just real values without
> imaginary part. I don't have any mathematical proof for this, but it
> probably wouldn't be too hard to find such.
>

I remembered again, it's called the complex conjugate.
http://en.wikipedia.org/wiki/Complex_conjugate

>
> *) adding another pole/zero for each complex one, like z=-j if you already
> have a z=j.
>
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