[PD] vcf~ producing output without input for 0Hz cutoff?

[Christof Ressi]

Just expand on Antoine's post, let's look at the formula of Pd's 1-pole 
lowpass filter:

k = freq * 2pi / sr

y[i] = x[i] * k + y[i-1] * (1 - k)

For freq=0 this becomes:

y[i] = y[i-1]

As you can see, this would just repeat the previous output infinitely, 
ignoring the input altogether. There is no decay to zero!

The same reasoning applies to bandpass filters such as [vcf~].

Christof

On 12.04.2024 09:10, cyrille henry wrote:
> I don't think it's weird for a lowpass filter to go under 20Hz. They 
> are not restricted to audio signals.
> I use them a lot to smooth control signals, or to replace line~.
> (I really hate line~ to control sound amplitude or preset transition, 
> it's way too robotic)
>
> cheers
> c
>
> Le 12/04/2024 à 08:01, Alexandre Torres Porres a écrit :
>> and you got a strong DC component over there :)
>>
>> anyway, it also seems weird to have a lowpass or a bandpass going as 
>> low as in the 20hz range. If you wanna do it just so it fades out to 
>> silence, you need a DC filter, something like a [hip~ 5] object, so 
>> when the lowpass, bandpass gets there, then you have nothing.
>>
>> cheers
>>
>> Em qui., 11 de abr. de 2024 às 15:40, Antoine Rousseau 
>> <antoine at metalu.net <mailto:antoine at metalu.net>> escreveu:
>>
>>     Well, let's simplify a bit, forget all the filter complexity (Q, 
>> slope, definition of the cutoff frequency...).
>>
>>     Let's just say that the output of a lowpass filter cannot move 
>> faster than the cutoff frequency: a 1Hz filter output cannot move 
>> faster than 1Hz (so it can't go back and forth in less than a second 
>> or so), a 1kHz can't go back and forth in less than about 1ms, etc. 
>> The output of a 0Hz filter can't move... at all. When you set the 
>> cutoff to 0Hz, the output freezes to its current value. It won't 
>> magically decay to 0.
>>
>>     Hey, if you set the framerate of a movie to 0 frame/second, it 
>> will just stop, and will show the same image forever; it won't fade 
>> to black!
>>
>>     Antoine
>>
>>
>>
>>     Le jeu. 11 avr. 2024 à 14:08, Peter P. <peterparker at fastmail.com 
>> <mailto:peterparker at fastmail.com>> a écrit :
>>
>>         * Antoine Rousseau <antoine at metalu.net 
>> <mailto:antoine at metalu.net>> [2024-04-11 13:40]:
>>          > That doesn't seem incorrect to me; after all, a lowpass 
>> filter at 0Hz
>>          > implies that its output is constant (any change would 
>> involve frequencies >
>>          > 0Hz).
>>
>>         Thanks Antoine,
>>
>>         Why does a lowpass filter, that has a cutoff frequency of 0Hz 
>> imply that
>>         it's output is constant?
>>
>>         I will describe the problem again hoping that I will 
>> understand it
>>         better myseld:
>>         I have an oscillating input signal that has some DC offset 
>> (unipolar
>>         sawtooth from phasor~). I fade this signal's amplitude to 
>> -inf dB using
>>         [line~].
>>
>>         I also fade down the filter cutoff (defined as the -3dB point 
>> of the
>>         filter curve) from 400Hz to 0Hz. The filter will then 
>> continue to produce an
>>         non-decaying output.
>>
>>         If I fade down the filter cutoff down to only 1Hz, it's 
>> output will decay (somehow
>>         counterintuitively to me). This is the part I don't get.
>>
>>         I understand that vcf~ is a resonant filter, and it can have 
>> a gain
>>         greater 1 around the cutoff frequency, especially for high Q 
>> values. The
>>         above behavior can also be observed for Q=1.
>>
>>         Thanks for all hints!
>>         Peter
>>
>>
>>
>>         _______________________________________________
>>         Pd-list at lists.iem.at <mailto:Pd-list at lists.iem.at> mailing list
>>         UNSUBSCRIBE and account-management -> 
>> https://lists.puredata.info/listinfo/pd-list 
>> <https://lists.puredata.info/listinfo/pd-list>
>>
>>     _______________________________________________
>>     Pd-list at lists.iem.at <mailto:Pd-list at lists.iem.at> mailing list
>>     UNSUBSCRIBE and account-management -> 
>> https://lists.puredata.info/listinfo/pd-list 
>> <https://lists.puredata.info/listinfo/pd-list>
>>
>>
>> _______________________________________________
>> Pd-list at lists.iem.at mailing list
>> UNSUBSCRIBE and account-management -> 
>> https://lists.puredata.info/listinfo/pd-list
>
>
>
> _______________________________________________
> Pd-list at lists.iem.at mailing list
> UNSUBSCRIBE and account-management -> 
> https://lists.puredata.info/listinfo/pd-list