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

Alexandre Torres Porres porres at gmail.com
Tue Sep 24 15:15:20 CEST 2013

```well, not sure what you mean, again way over my head, but I was giving it a
hard shot in the dark and it seemed to have worked out :)

I just summed both parts of Z0, for instance, and tried the given math,
numbers came out!

now to make more tests and see if this is consistent, then finish the patch
;)

thanks!

2013/9/24 Funs Seelen <funsseelen at gmail.com>

> 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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