# [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 14:50:12 CEST 2013

```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)

cheers!

2013/9/24 Alexandre Torres Porres <porres at gmail.com>

>
> > This is the online tool:
> http://kmt.hku.nl/~pieter/cgi-bin/resp/nph-PZT.cgi.
>
> damn, it says it cant load it here :P
>
> but this seems like a simple formula to try out, from what you copied
> here. If that's all, and if I got what it means, I can see a patch coming
> right now :) let's see!
>
> thanks
>
>
> 2013/9/24 Funs Seelen <funsseelen at gmail.com>
>
>> Hi Alexandre,
>>
>> This is the online tool:
>> http://kmt.hku.nl/~pieter/cgi-bin/resp/nph-PZT.cgi.
>>
>> It starts with an example and every time you refresh the page it gives
>> you a new one. If you scroll down there's a link that tells you how the
>> coefficients were calculated, e.g.:
>> 2 zeros give 3 coefficients: *a0* = G
>> *a1* = -G(Z0 + Z1)
>> *a2* = G(Z0*Z1)
>>
>> 2 poles give 3 coefficients: *b0* = 1
>> *b1* = -(P0 + P1)
>> *b2* = (P0*P1)
>>
>> The linear difference equation is derived from these as you can see.
>>
>> Regards,
>> --Funs
>>
>>
>> On Tue, Sep 24, 2013 at 7:36 AM, Alexandre Torres Porres <
>> porres at gmail.com> wrote:
>>
>>> for what i see, it's not some sort of straight formula, right? seems a
>>> bit more complicated than that.
>>>
>>> cheers
>>>
>>>
>>> 2013/9/23 Funs Seelen <funsseelen at gmail.com>
>>>
>>>> On Mon, Sep 23, 2013 at 5:35 PM, Alexandre Torres Porres <
>>>> porres at gmail.com> wrote:
>>>>
>>>>>
>>>>> thanks, here's a pic of what I have so far
>>>>>
>>>>>
>>>>> https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn1/11212_10151872996046683_1825736206_n.jpg
>>>>>
>>>>
>>>> Cool.
>>>>
>>>>
>>>>>
>>>>> > For extra inspiration you could have a look at PoZeTools
>>>>>
>>>>> It sure does look like what I need. Thanks. But extracting what I need
>>>>> to know about the math of converting from coordinates to coefficients was
>>>>> just over my head :P unfortunately, sorry.
>>>>>
>>>>> I was hoping for something simpler, like just the operations needed.
>>>>> If the info is in code, I need it to more explicit. I'd really appreciate
>>>>> if anyone knows how to read from this and just points it out for me so I
>>>>> can put it in a patch.
>>>>>
>>>>> I'm assuming it's rather simple math
>>>>>
>>>>
>>>> I remember I once learned how to do this but never repeated the
>>>> practice. If I find time to do that I would gladly try to figure it out
>>>> again, but if someone more experienced feels the urge to chime in before
>>>> that time I would be very happy too :).
>>>>
>>>
>>>
>>
>
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