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

Funs Seelen funsseelen at gmail.com
Tue Sep 24 19:55:31 CEST 2013

```On Tue, Sep 24, 2013 at 6:32 PM, Simon Wise <simonzwise at gmail.com> wrote:

> On 24/09/13 21:46, Funs Seelen wrote:
>
>> On Tue, Sep 24, 2013 at 3:35 PM, Alexandre Torres Porres
>> <porres at gmail.com>wrote:
>>
>>  so you're basically saying all i need to use is use only the real part,
>>> right?
>>>
>>>
>> No, I meant that I have the idea that the imaginary part in the calculated
>> coefficients will disappear automatically if you add complex conjugates
>> for
>> all poles and zeros, probably when somehow i^2 gets -1 somewhere. But I
>> must say I'm not a mathematician and not sure at all.
>>
>
> indeed it will ... a conjugate is the number with the imaginary part
> negated ... so adding a number and its conjugate will certainly end up with
> a real part only.
>

Yes, true, and the imaginary part disappears as well when multiplying if
the real parts are equal, e.g.:

i^2 = -1, so ...

(0.5 + 0.5i) * (0.5 - 0.5i) = 0.25 + 0.25i - 0.25i - 0.25i^2 = 0.5

>
>
> Simon
>
>
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