[PD] bandpass or resonant?

Alexandre Torres Porres porres at gmail.com
Tue Jan 13 16:48:59 CET 2015 

This bit of the wikipedia article on resonance about "Q" (
http://en.wikipedia.org/wiki/Resonance#Q_factor ) mentions a lot of what we
read about "Ringing Filter", and how a higher Q will make it "ring"
longer... this is what you get from that bandpass in the EQ Cookbook that
says it has "constant skirt gain, peak gain = Q" - or what I'm assuming to
be a "resonant filter by excellence" or whatever...

cheers



2015-01-13 13:38 GMT-02:00 Alexandre Torres Porres <porres at gmail.com>:

> "*Ultimately I think "resonant" is a general descriptive term for
> filters, that shouldn't be interpreted as a detail of implementation.*"
>
> I guess you have a point there, and I was also driving to this conclusion.
>
> "*It sounds like the Resonz UGen in supercollider is exactly what Julius
> Smith is talking about in that description of the two-pole filter.*"
>
> Actually, the Resonz UGen is a Two Pole / Two Zero filter, which is very
> more closely related to [cyclone/reson~].
>
> A Two-Pole only filter (no zeros) like the one Julius is describing is
> actually what the [bp~] object is!
>
> "*But then there's the other supercollider filter UGens with "resonant"
> in the name, which seem more like what Martin was describing - RLPF
> (resonant low-pass filter) for example is a low-pass filter where you can
> adjust the resonance near the cutoff.* "
>
> Yep, and this is also much like the [cyclone/lores~] object in Pd. Check
> that patch I sent for more detailed info on these filters.
>
> I've always assumed that a filter, in order to be called a "resonant
> filter" or a "resonator" - being it a low pass, a high pass or a band pass
> -, needed to boost/add gain to a particular cutoff frequency (in the case
> of lowpass and highpas - which is the case for [lores~] or RLPF) or add
> gain to some center frequency (in the case of a bandpass) - which is also
> called "resonant frequency".
>
> The quote from Julius in that link - where he says "*A resonator is a
> recursive filter that boosts signal amplitude at a particular frequency*"
> - is in line with my assumption.
>
> But the concept of resonance in physics, in its utmost purity according to
> wikipedia, is that it "is the tendency of a system to oscillate with
> greater amplitude at some frequencies than at others". Meaning that it
> doesn't really have to add gain to something, but only favor a frequency
> amongst others... In this context, a bandpass - in general - is a
> "resonator"...
>
> But it'd be cool if I could find a definitive word about this in the
> filter literature!
>
> Cheers
>
> 2015-01-13 13:16 GMT-02:00 Brian Fay <ovaltinevortex at gmail.com>:
>
> It sounds like the Resonz UGen in supercollider is exactly what Julius
>> Smith is talking about in that description of the two-pole filter.
>>
>> But then there's the other supercollider filter UGens with "resonant" in
>> the name, which seem more like what Martin was describing - RLPF (resonant
>> low-pass filter) for example is a low-pass filter where you can adjust the
>> resonance near the cutoff. I haven't played with this too much myself, but
>> I'm guessing with the right Q value you could drive this to
>> self-oscillation?
>>
>> Ultimately I think "resonant" is a general descriptive term for filters,
>> that shouldn't be interpreted as a detail of implementation.
>>
>> On Tue, Jan 13, 2015 at 9:28 AM, Alexandre Torres Porres <
>> porres at gmail.com> wrote:
>>
>>> I'm pending to say that there is no real distinction between "Resonant
>>> filter" and a "resonator", and a "bandpass" can be implicitly thought of as
>>> a resonator. Here's what I also found in Julius' website
>>>
>>>
>>> https://ccrma.stanford.edu/~jos/filters/First_Order_Complex_Resonators.html
>>>
>>> Pass the mouse cursor over the "Resonator" over the title "First-Order
>>> Complex Resonators
>>> <https://ccrma.stanford.edu/~jos/filters/Two_Pole.html>" to see the
>>> popup (also attached).
>>>
>>> cheers
>>>
>>> 2015-01-13 1:20 GMT-02:00 Martin Peach <chakekatzil at gmail.com>:
>>>
>>> I was looking at circuit diagrams for analog synthesizers recently and
>>>> noticed that the "resonance" control is nothing more than feeding some
>>>> fraction of the output back to the input. With more feedback oscillation
>>>> occurs at the cutoff frequency for any type of filter, highpass, bandpass
>>>> or lowpass.
>>>>
>>>> Martin
>>>>
>>>>
>>>> On Mon, Jan 12, 2015 at 9:09 PM, Alexandre Torres Porres <
>>>> porres at gmail.com> wrote:
>>>>
>>>>> Nice I give an impression to be an expert, but filters is just
>>>>> something I've actually recently started studying :)
>>>>>
>>>>> > I'm wondering if by "resonant" filter you mean the
>>>>> > same thing as "resonator" filter?
>>>>>
>>>>> Now you got me... good question, and I'm not sure, haha. The link
>>>>> looks nice btw, will definitely check it. Thanks.
>>>>>
>>>>> So now I'm even more confused. Is "resonant filter" and "resonator"
>>>>> two different concepts? Maybe I'm having trouble with the english
>>>>> nomenclature and everything.
>>>>>
>>>>> To be honest and more detailed about the issues I'm encountering, I
>>>>> ask this based on another topic I was discussing with Julius Smith in the
>>>>> Supercollider list, but it went dead and I got no replies. In it I was
>>>>> asking if the object "Resonz" should really be called a "Resonant filter",
>>>>> because it was just a bandpass filter in my opinion. Then Julius was
>>>>> mentioning how "*A resonator is a special case of a passband filter
>>>>> having a nearly zero-width passband.*"
>>>>>
>>>>> I see he used the term "resonator" and not "Resonant Filter" (as
>>>>> Resonz is described). So yeah, now I'm more confused... is resonator the
>>>>> same as resonant or what?
>>>>>
>>>>> But anyway, we can bring the discussion into the Pd world, and talk
>>>>> about the [reson~] object, as I will do later on.
>>>>>
>>>>> I was googling and saw how the term resonant filter could be used to
>>>>> describe a regular bandpass filter. And how the bandpass' center frequency
>>>>> could also be called "resonant frequency". So they might be used in the
>>>>> same way... (accurately or not).
>>>>>
>>>>> Now here is my opinion. Just like a resonant low pass filter (the
>>>>> [lores~] object in Pd), the concept of resonance in a filter relates to how
>>>>> it adds gain around the resonant frequency.
>>>>>
>>>>> In the Audio-EQ-Cookbook (link:
>>>>> http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt ) that presents
>>>>> formulas for biquad coeficients you have two different bandpass filters,
>>>>> lets call them BPF1 and BPF2. So, BPF2 has "constant 0 dB peak gain",
>>>>> meaning it doesn't affect anything arounf the center frequency. Now BPF1
>>>>> says it has "constant skirt gain, peak gain = Q", meaning that the Q
>>>>> or bandwidth controls the gain of the filter. I consider BPF2 to be a
>>>>> regular bandpass filter, whereas BPF1, which adds gain for narrower
>>>>> bandwidths, seems to be a "resonant" one... (which makes me think Resonz
>>>>> shouldn't be described as resonant filter, as it's just a bandpass, or
>>>>> "BPF2").
>>>>>
>>>>> Oh, there's another term around, the "ringing" filter, which seems to
>>>>> be another term for resonant filter. In SuperCollider they have Ringz,
>>>>> which was supposed to be the same as Resonz object (or a resonant filter
>>>>> for that matter), but they are different like the two different kinds of
>>>>> bandpass in the EQ Cookbook (Ringz = BPF1 / Resonz = BPF2).
>>>>>
>>>>> Coming into the Pd world we can talk about the [reson~] object. As the
>>>>> name implies, it is a resonant filter. But the helpfile says it is a "Bandpass
>>>>> filter" (damn). Funny enough, in Max, the [reson~] object is said to be
>>>>> indded a *Resonant Bandpass Filter*. So maybe we should update [reson~]'s
>>>>> help file in Pd... But the deal is: [reson~] is actually a bandpass like
>>>>> BFP2 or Resonz, but it has a separate parameter for the gain. Meaning it
>>>>> works basically as a bandpass filter, where changing the Q doesn't affect
>>>>> the gain. But you can also give it a boost or a cut with the gain
>>>>> parameter. By giving it a boost it would behave in a way that I'm
>>>>> considering to be an actual "resonant" filter.
>>>>>
>>>>> Now let me go ahead and share a patch that I'm writing for my computer
>>>>> music classes. It's about several filters that can be obtained with biquad.
>>>>> So I present Pd's vanilla filters such as [lop~], [hip~] and [bp~]. I also
>>>>> present externals like [lores~] and [reson~] and I do present all the
>>>>> filters from the Audio Eq Cookbook as well. It's in portuguese, and part of
>>>>> a big series of examples, but what the hell...
>>>>>
>>>>> By the way, I was also able to implement Resonz and Ringz as [biquad~]
>>>>> in Pd, but I don't have it on this example (but to hell with supercollider
>>>>> already, hehe).
>>>>>
>>>>> So there you can check the behaviour and differences that I've
>>>>> pointed. For [reson~], I have two separate parameters, one is for "Q", and
>>>>> the other one, which is originally "gain", I'm calling the "resonance"
>>>>> parameter. Much like the resonance parameter in [lores~]...
>>>>>
>>>>> As for the Cookbook filters, BPF2 is what I'm calling a regular
>>>>> "bandpass", and it has a parameter of "Q". As for BPF1, I'm calling it a
>>>>> "resonant filter", and it has a parameter of "resonance" instead of "Q"
>>>>> (but the idea is that more Q gives more gain/resonance).
>>>>>
>>>>> I hope I'm clear in the midst of so much detail and information. It's
>>>>> just a stupid doubt on the nomenclature of filters, but this kind of issue
>>>>> can be quite a pain in the ass, and the subject of many confusions.
>>>>>
>>>>> So, in short, I still keep my original question: Are bandpass and
>>>>> resonant filters the same? Or is there a difference between calling one a
>>>>> resonant and not a bandpass? Moreover, what about a resonator? Is my
>>>>> assumption on how to call one a bandpass and a resonant correct or it
>>>>> doesn't have anything to do with the official literature? And how about
>>>>> what Julius Smith had to say?
>>>>>
>>>>> Cheers
>>>>>
>>>>> 2015-01-12 20:03 GMT-02:00 Brian Fay <ovaltinevortex at gmail.com>:
>>>>>
>>>>> Based on your posts in this group, you definitely know more about
>>>>>> filters than I do, so I don't really have an answer to this question - but
>>>>>> I'm wondering if by "resonant" filter you mean the same thing as
>>>>>> "resonator" filter?
>>>>>>
>>>>>> I saw something interesting earlier today about using resonator
>>>>>> filters as control sources for FM synthesis:
>>>>>> http://tai-studio.org/index.php/projects/sound-programming/complexres/
>>>>>>
>>>>>> The paper that is linked in the article has some details on the
>>>>>> mathematical implementation of the filter, but that's mostly mumbo-jumbo to
>>>>>> me.
>>>>>>
>>>>>> On Mon, Jan 12, 2015 at 4:24 PM, Alexandre Torres Porres <
>>>>>> porres at gmail.com> wrote:
>>>>>>
>>>>>>> Hi, are bandpass and resonant filters the same? Or is there a
>>>>>>> difference between calling one a resonant and not a bandpass?
>>>>>>>
>>>>>>> thanks
>>>>>>>
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>>
>
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