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

Funs Seelen funsseelen at gmail.com
Tue Sep 24 15:08:38 CEST 2013

```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.

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