Since there's been quite some discussion on this subject, I'll bump in to share eight externals I wrote, based on Mike Moser-Booth's (mmb) [flitercoeff.mmb~] and [biquad.mmb~] abstractions.
The objects are: [lowPass~], [bandPass~], [highPass~], [allPass~], [resonant~], [lowShelf~], [peakNotch~] and [highShelf~]. They all have only signal inlets to avoid clicks when changing parameters. You can get them here http://drymonitis.me/code/ look for the "Various filters" link.
The .zip file contains binaries for OS X and Linux, help patches (dunno if they are very helpful), source code, Pd's generic Makefile and a README.
Comments are welcome.


On Thu, Jul 24, 2014 at 8:40 PM, Alexandre Torres Porres <porres@gmail.com> wrote:
> whether a [cpole~] filter like [vcf~] could be obtained with [biquad~].

I meant at least the real output of [vcf~]


2014-07-24 14:28 GMT-03:00 Alexandre Torres Porres <porres@gmail.com>:

yep, totally makes perfect sense to me now that it is a [cpole~].

I guess you can consider (ampcorrect * oneminusr) as a gain factor and multiply the input signal by this much before getting it to a [cpole~] with the same coefficients, and voilá... although getting all these coefficients to come up in a vanilla patch seems a lot of trouble...

But what I'm really and still dying to learn/figure out is whether a [cpole~] filter like [vcf~] could be obtained with [biquad~]. My intuition said: Yes. But after a few experiments I'm changing my mind... Can anyone just confirm me that?

What drove my intuition is the attached patch, which is a biquad~ filter made of raw filters I derived from mmb's work. If it made any sense is because it is implemented with [cpole~] and [czero~] objects, so it seemed that a set of biquad coefficients could result in just a couple of coefficients for one [cpole~]. But then, by checking it out and trying to do it, it doens't seem possible to get a coordinate pair for a [cpole~] with biquad coefficients... hmmm, bummer.

Any thoughts?

thanks


2014-07-24 13:33 GMT-03:00 Miller Puckette <msp@ucsd.edu>:

Yep, vcf~ isn't a 2-pole real filter but a 1-pole complex one (although
its second outlet -- I think -- should be similar to a 2-pole real
filter's output in theory, but in reality should be numerically more precise.)

I'll change the comment to something vaguer and more descriptive in the
code..

Unless I'm badly mistaken, vcf~ is simply a cpole~ with extra stuff to compute
the coefficient built in.  There's no 'x2' because the input is taken to be
real-valued.

cheers
M

On Thu, Jul 24, 2014 at 01:18:28PM -0300, Alexandre Torres Porres wrote:
> >> The real part may be used as a resonant
> >> bandpass filter and the imaginary as a
> >> resonant low-pass filter, but they can be
> >> combined to make other possibilities."
>
> > what sort of possibilities???
>
> I wouldn't expect much about this. I guess it's like any other filters that
> can be combined in many ways.
>
> Another thing I wanted to inquire is about bp~ having a frequency response
> that is not symmetric. The lower part of the spectrum has more energy.
> Could one consider it more of a "resonant low-pass filter", similar to
> [vcf~]'s second outlet?
>
> By the way, while we're at it, I'd like to share something that may not be
> too important, but it's related. I was able to implement [cpole~] in
> [fexpr~]. Here it goes:
>
> expr 1:
>
> [fexpr~ $x1 + ($x3 * $y1) - ($x4 * $y2);
> $x2 + ($x4 * $y1) + ($x3 * $y2)]
>
> if we consider $x3 and $x4 as variables named, respectively, coefr
> (coeficient for the real part) and coefi (coeficient for the imaginary
> part), we then have:
>
> expr 2:
>
> *[fexpr~ $x1 + (coefr * $y1) - (coefi * $y2);*
> *$x2** + (*coefi * $y1) + (coefr * $y2)]
>
> Now, by checking the code of [vcf~] I was able to narrow down to its core
> formula, which is something like this
>
> expr 3:
>
> *ampcorrect * oneminusr* * *f1 + (coefr * re2) - (coefi * im)*;
> *(coefi * re2) + (coefr * im)*
>
> the bolded letters in "expr 3" seem to match perfectly to "expr 2". The
> differences are underlined ($x2 in expr 2 and ampcorrect/oneminusr in expr
> 3).
>
> That gets me closer to being able to implement [vcf~] with a [cpole~] I
> guess, but I find it weird that the imaginary output does not have the $x2
> signal input to be added to the rest of the expression. I worry that
> actually prevents it from being successfully implemented with [cpole~]. Am
> I missing something?
>
> Anyway, the thing is that I'm still really curious to learn wether vcf~ is
> a "two pole" filter or a "one complex pole" filter, and the reason behind
> it is because I believe we could make a biquad~ version of [vcf~] (at least
> for its real output). That's the bottom line.
>
> cheers
>
>
>
>
> 2014-07-24 6:45 GMT-03:00 i go bananas <hard.off@gmail.com>:
>
> > just chipping in with my 2 cents that it would be fantastic to get more
> > documented info on all this.
> >
> > especially curious about:  "but they can be combined to make other
> > possibilities."
> >
> > what sort of possibilities???
> >
> >
> > On Thu, Jul 24, 2014 at 5:07 PM, Alexandre Torres Porres <porres@gmail.com
> > > wrote:
> >
> >> Hi Miller, still trying to get my head around this. But anyway, one thing
> >> I have to note is that the source code of [vcf~] says it is a "two pole
> >> filter", not a "one complex pole" filter.
> >>
> >> Should that description be changed? If not, why?
> >>
> >> thanks
> >>
> >>
> >> 2014-04-12 14:13 GMT-03:00 Miller Puckette <msp@ucsd.edu>:
> >>
> >> Yep - vcf~ is essentially a wrapper for cpole~.
> >>>
> >>> cheers
> >>> M
> >>>
> >>> On Sat, Apr 12, 2014 at 02:10:19PM -0300, Alexandre Torres Porres wrote:
> >>> > that's great to know, thanks!
> >>> >
> >>> > Let me just see if I get a bit of the theory. Can I get [vcf~] with
> >>> just
> >>> > one [cpole~] object and the right coeficients?
> >>> >
> >>> > Cheers
> >>> >
> >>> >
> >>> > 2014-04-12 13:36 GMT-03:00 Miller Puckette <msp@ucsd.edu>:
> >>> >
> >>> > > They're quite different.  bp~ is the cheapest possible bandpass
> >>> filter
> >>> > > (as far as I know).  vcf~ is a one-pole complex filter whose outputs
> >>> are
> >>> > > the real and imaginry parts.  The real part may be used as a resonant
> >>> > > bandpass filter and the imaginary as a resonant low-pass filter, but
> >>> > > they can be combined to make other possibilities.
> >>> > >
> >>> > > It's possible to graph their frequency responses using the help patch
> >>> > > "H10.measurement.pd' in 3.audio.examples.
> >>> > >
> >>> > > cheers
> >>> > > Miller
> >>> > >
> >>> > > On Sat, Apr 12, 2014 at 04:28:11AM -0300, Alexandre Torres Porres
> >>> wrote:
> >>> > > > Hi there, who can confirm that both [bp~] and [vcf~] are exactly
> >>> the
> >>> > > really
> >>> > > > same thingy? The code looks quite different...
> >>> > > >
> >>> > > > Moreover, why the two outlets for vcf~? Help doesn't say anything.
> >>> > > >
> >>> > > > Thanks
> >>> > >
> >>> > > > _______________________________________________
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> >>>
> >>
> >>
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