[PD] biquad~ with elementary filters [was: Re: dinosaurs ...]
Claude Heiland-Allen
claudiusmaximus at goto10.org
Mon Sep 15 11:45:39 CEST 2008
Claude Heiland-Allen wrote:
> Frank Barknecht wrote:
>> Hallo,
>> martin brinkmann hat gesagt: // martin brinkmann wrote:
>>
>>> Claude Heiland-Allen wrote:
>>>
>>>> cpole~ czero~ rpole~ rzero~ have signal inlets for filter control, so i
>>>> assume sufficiently smooth changes will not cause clicks
>>> that is true, but it looks like no one has made a (usual lp,hp,etc.)
>>> filter with these objects until now.
>> Except Miller. [1]
>>
>> Though I agree that some more of these would be handy. I tried to make
>> a biquad~ clone with the elementary filters, but failed so far. I
>> assume from [2] that the transfer function of two rzero~ and two
>> rpole~ in series should be the same as a biquad~,
>
> You need two cpole~ and two czero~ here, admittedly in complex-conjugate
> pairs.
(oops) : either conjugate pairs, or both on the real line.
>
>> however I don't know
>> how to convert the ff1, ff2, ff3, fb1 and fb2 coefficients of biquad~
>> into the coefficients to use at the second inlets of the elemetary
>> filters. Can anyone help?
>
> http://ccrma.stanford.edu/~jos/filters/BiQuad_Section.html
>
> you need to munge the biquad coefficients from the form expected by Pd's
> biquad~ to the form of the difference equation at the bottom - should
> just be some scaling and sign stuff.
>
> then you can factorize the transfer function's numerator and denominator
> to get the locations of the (complex) zeroes and poles (using the
> quadratic formula would do the trick)
>
> then feed them to [czero~] [cpole~], and an additional [*~] for the
> global gain.
>
>> [1] http://crca.ucsd.edu/~msp/techniques/latest/book-html/node160.html
>> [2] http://crca.ucsd.edu/~msp/techniques/latest/book-html/node136.html
>>
>> Ciao
>
>
> Claude
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