[music-dsp] What is resonance?

[Mehdi Touzani]

Hi all,
I follow the llist for a while, but I am not a DSP programmer, I do DSP
audio apps for about 20 years now, for sonic core plateform "Scope" and
Xite". I begin with other things like juce or flowstone, but so far,
scope is still far superior in terms of sound results. Too bad there is no
scripting tool for it (well there is but it is not available to me).

My question is probably weird for you - like super noob - , because i am
NOT looking for math or codes, but hints about a general
design/architecture.

So... how do you do a resonance in a lowpass circuit? :-) not the math,
not the code, just the architecture.

Personnally, i came to the conslusion that some kind of very short delay
with feedback, mixed in parallel with the non resonance low pass sound,
could do the trick. . The more feedback, the more resonance, and with
feedback over -6dB, it would begin to self resonate.

But it is having the resonance in parralel to a dry sound that bothers me;
but may be that's the only way to do ?

I have read about hardware filters and ok, there is math, but there is also
the effect of the hardware components. Some articles even suggest that a
bandpass in parralel could do the trick : or more exactly, a bandpass
fonction is created after the resonance, to remove frequencies that would
overlap with the cutoff.


So, any hints that could help me improve the process etc would be very
welcome.

Thanks

Mehdi

[STEFFAN DIEDRICHSEN]

The resonance in low pass filter with an order greater than 2 is basically just a feedback from the output to the input. You need to switch the polarity of the signal, in other words, you subtract the output from the input, in order to place the feedback point to the point, where the phase shift of the low pass filter is 180 degrees.

Hope this helps you to get started.

Best,

Steffan

Von meinem iPad gesendet

Post by Mehdi Touzani
Hi all,
I follow the llist for a while, but I am not a DSP programmer, I do DSP audio apps for about 20 years now, for sonic core plateform "Scope" and Xite". I begin with other things like juce or flowstone, but so far, scope is still far superior in terms of sound results. Too bad there is no scripting tool for it (well there is but it is not available to me).
My question is probably weird for you - like super noob - , because i am NOT looking for math or codes, but hints about a general design/architecture.
So... how do you do a resonance in a lowpass circuit? :-) not the math, not the code, just the architecture.
Personnally, i came to the conslusion that some kind of very short delay with feedback, mixed in parallel with the non resonance low pass sound, could do the trick. . The more feedback, the more resonance, and with feedback over -6dB, it would begin to self resonate.
But it is having the resonance in parralel to a dry sound that bothers me; but may be that's the only way to do ?
I have read about hardware filters and ok, there is math, but there is also the effect of the hardware components. Some articles even suggest that a bandpass in parralel could do the trick : or more exactly, a bandpass fonction is created after the resonance, to remove frequencies that would overlap with the cutoff.
So, any hints that could help me improve the process etc would be very welcome.
Thanks
Mehdi
_______________________________________________
dupswapdrop: music-dsp mailing list
https://lists.columbia.edu/mailman/listinfo/music-dsp

[Spencer Jackson]

Resonance is the characteristic of some systems to store and release energy
at particular frequencies. It's not limited to filters, mechanical systems
like springs or pendulums have resonance (get on a swing at the park and
try to change your frequency and you'll feel the effects of resonance).

In an electrical system, a minimal passive resonant circuit would be one
with 2 capacitors and 2 resistors. Selecting the values of the components
determines the frequency, but what happens is that at a certain frequency
the energy gets stored and passed back and forth between the capacitors,
like the swing going back and forth. This storage and energy swapping
emphasizes that frequency. Depending on the "Quality factor" or amount of
resonance that frequency can become much more apparent than the other
frequencies in the signal even if the input is wide-band.

When you are talking about delay and feedback, you are creating a digital
filter, but I think it is worthwhile to spend some time understanding the
theoretical concept and think in terms of energy and frequency. Your
feedback delay becomes the storage and certain frequencies will resonate
with that system.

Post by Mehdi Touzani
But it is having the resonance in parralel to a dry sound that bothers

me; but may be that's the only way to do ?

I'm not sure what you mean but I think you need some study in filter
design, because a single feedback delay causes comb filtering but its not a
classical lowpass. Is that what you are trying to achieve? Digital filters
are almost universally combinations of short delays (typically 1 sample)
placed in different patterns and fed back in different amounts (e.g.
https://en.wikipedia.org/wiki/Digital_filter#Filter_realization).

Here are some resources that may help you:
http://www.dspguide.com/ch14.htm
https://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/VAFilterDesign_2.0.0a.pdf

That first one is a book that can help you more with the fundamentals in
the early chapters as well. I hope this is somewhat helpful, if not perhaps
I need to understand better specifically what you are trying to achieve.
_Spencer

Post by Mehdi Touzani
Hi all,
I follow the llist for a while, but I am not a DSP programmer, I do DSP
audio apps for about 20 years now, for sonic core plateform "Scope" and
Xite". I begin with other things like juce or flowstone, but so far,
scope is still far superior in terms of sound results. Too bad there is no
scripting tool for it (well there is but it is not available to me).
My question is probably weird for you - like super noob - , because i am
NOT looking for math or codes, but hints about a general
design/architecture.
So... how do you do a resonance in a lowpass circuit? :-) not the
math, not the code, just the architecture.
Personnally, i came to the conslusion that some kind of very short delay
with feedback, mixed in parallel with the non resonance low pass sound,
could do the trick. . The more feedback, the more resonance, and with
feedback over -6dB, it would begin to self resonate.
But it is having the resonance in parralel to a dry sound that bothers me;
but may be that's the only way to do ?
I have read about hardware filters and ok, there is math, but there is
also the effect of the hardware components. Some articles even suggest that
a bandpass in parralel could do the trick : or more exactly, a bandpass
fonction is created after the resonance, to remove frequencies that would
overlap with the cutoff.
So, any hints that could help me improve the process etc would be very
welcome.
Thanks
Mehdi
_______________________________________________
dupswapdrop: music-dsp mailing list
https://lists.columbia.edu/mailman/listinfo/music-dsp

[Andrew Simper]

Resonance is just delay with feedback. Resonance occurs when you delay a
signal and then feed it back with some gain to the input of the delay "in
phase" with the original input, which means the delayed signal adds
together and boosts the input level to the delay. If you use a normal
digital delay line you get what is called a linear phase delay, so each
frequency is delayed by the same amount. If you use an IIR filter to delay
the signal you get what is called a non-linear phase delay, so each
frequency is delayed by a different amount. The particular arrangement of
multiple stages of delays and how the feedback is arranged both around
individual stages and globally all determine the structure of the filter,
and the type of filtering achieved.

Most synth filters use IIR filters. The amount of non-linear phase delay is
typically referred to in terms of degrees, as this is usually more useful
for filter design. When the signal has been delayed 360 degrees at a
particular frequency, if you add this to the input signal you get a boost
in amplitude of that frequency since it is back in phase with the input,
which is called constructive interference. With enough feedback gain a
resonant peak will form as the constructive interference is in a feedback
loop with itself. Most resonant filter designs use the fact that taking the
negative of a signal actually changes the phase by 180 degrees at all
frequencies. So most filters delay the phase of the signal by 180 degrees
somehow, then subtract this from the input with some gain (negative
feedback) and so form a resonant peak.

Many people have spent a lot of time forming many types of low pass
resonant filter structures. In synths it is mostly the non-linear
properties that very between different filters, there are actually only 3
structures typically used to form low pass resonant filters: multiple IIR
one pole integrators with feedback (svf) or multiple IIR one pole low pass
filters with feedback (sallen key, cascade).

Andy

Post by Spencer Jackson
Resonance is the characteristic of some systems to store and release
energy at particular frequencies. It's not limited to filters, mechanical
systems like springs or pendulums have resonance (get on a swing at the
park and try to change your frequency and you'll feel the effects of
resonance).
In an electrical system, a minimal passive resonant circuit would be one
with 2 capacitors and 2 resistors. Selecting the values of the components
determines the frequency, but what happens is that at a certain frequency
the energy gets stored and passed back and forth between the capacitors,
like the swing going back and forth. This storage and energy swapping
emphasizes that frequency. Depending on the "Quality factor" or amount of
resonance that frequency can become much more apparent than the other
frequencies in the signal even if the input is wide-band.
When you are talking about delay and feedback, you are creating a digital
filter, but I think it is worthwhile to spend some time understanding the
theoretical concept and think in terms of energy and frequency. Your
feedback delay becomes the storage and certain frequencies will resonate
with that system.

Post by Mehdi Touzani
But it is having the resonance in parralel to a dry sound that bothers

me; but may be that's the only way to do ?
I'm not sure what you mean but I think you need some study in filter
design, because a single feedback delay causes comb filtering but its not a
classical lowpass. Is that what you are trying to achieve? Digital filters
are almost universally combinations of short delays (typically 1 sample)
placed in different patterns and fed back in different amounts (e.g.
https://en.wikipedia.org/wiki/Digital_filter#Filter_realization).
http://www.dspguide.com/ch14.htm
https://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/VAFilterDesign_2.0.0a.pdf
That first one is a book that can help you more with the fundamentals in
the early chapters as well. I hope this is somewhat helpful, if not perhaps
I need to understand better specifically what you are trying to achieve.
_Spencer

Post by Mehdi Touzani
Hi all,
I follow the llist for a while, but I am not a DSP programmer, I do DSP
audio apps for about 20 years now, for sonic core plateform "Scope" and
Xite". I begin with other things like juce or flowstone, but so far,
scope is still far superior in terms of sound results. Too bad there is no
scripting tool for it (well there is but it is not available to me).
My question is probably weird for you - like super noob - , because i am
NOT looking for math or codes, but hints about a general
design/architecture.
So... how do you do a resonance in a lowpass circuit? :-) not the
math, not the code, just the architecture.
Personnally, i came to the conslusion that some kind of very short
delay with feedback, mixed in parallel with the non resonance low pass
sound, could do the trick. . The more feedback, the more resonance, and
with feedback over -6dB, it would begin to self resonate.
But it is having the resonance in parralel to a dry sound that bothers
me; but may be that's the only way to do ?
I have read about hardware filters and ok, there is math, but there is
also the effect of the hardware components. Some articles even suggest that
a bandpass in parralel could do the trick : or more exactly, a bandpass
fonction is created after the resonance, to remove frequencies that would
overlap with the cutoff.
So, any hints that could help me improve the process etc would be very
welcome.
Thanks
Mehdi
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dupswapdrop: music-dsp mailing list
https://lists.columbia.edu/mailman/listinfo/music-dsp

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dupswapdrop: music-dsp mailing list
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[Mehdi Touzani]

Hi !

Thanks a lot for all your replies.
Yes it helps a lot to get started on the right track.
It also gives me good direction to dig to improve the basic results and
achieve a "personal sound design" (something different than the ready-made
filters that I have).
At least to try something with low level building blocks.

Post by Mehdi Touzani
But it is having the resonance in parralel to a dry sound that bothers

me; but may be that's the only way to do ?

Post by Mehdi Touzani

Post by Spencer Jackson

Post by Mehdi Touzani

Post by Spencer Jackson
I'm not sure what you mean but I think you need some study in filter

design
Sorry about that : I was refering to a lowpass+bandpass in parallel, but
only the band pass would resonate.
But in fact I know the result sounds like two parralel filters :-) and is
not the right way to do it.

Thanks.

Mehdi

Post by Mehdi Touzani
Resonance is just delay with feedback. Resonance occurs when you delay a
signal and then feed it back with some gain to the input of the delay "in
phase" with the original input, which means the delayed signal adds
together and boosts the input level to the delay. If you use a normal
digital delay line you get what is called a linear phase delay, so each
frequency is delayed by the same amount. If you use an IIR filter to delay
the signal you get what is called a non-linear phase delay, so each
frequency is delayed by a different amount. The particular arrangement of
multiple stages of delays and how the feedback is arranged both around
individual stages and globally all determine the structure of the filter,
and the type of filtering achieved.
Most synth filters use IIR filters. The amount of non-linear phase delay
is typically referred to in terms of degrees, as this is usually more
useful for filter design. When the signal has been delayed 360 degrees at a
particular frequency, if you add this to the input signal you get a boost
in amplitude of that frequency since it is back in phase with the input,
which is called constructive interference. With enough feedback gain a
resonant peak will form as the constructive interference is in a feedback
loop with itself. Most resonant filter designs use the fact that taking the
negative of a signal actually changes the phase by 180 degrees at all
frequencies. So most filters delay the phase of the signal by 180 degrees
somehow, then subtract this from the input with some gain (negative
feedback) and so form a resonant peak.
Many people have spent a lot of time forming many types of low pass
resonant filter structures. In synths it is mostly the non-linear
properties that very between different filters, there are actually only 3
structures typically used to form low pass resonant filters: multiple IIR
one pole integrators with feedback (svf) or multiple IIR one pole low pass
filters with feedback (sallen key, cascade).
Andy

Post by Spencer Jackson
Resonance is the characteristic of some systems to store and release
energy at particular frequencies. It's not limited to filters, mechanical
systems like springs or pendulums have resonance (get on a swing at the
park and try to change your frequency and you'll feel the effects of
resonance).
In an electrical system, a minimal passive resonant circuit would be one
with 2 capacitors and 2 resistors. Selecting the values of the components
determines the frequency, but what happens is that at a certain frequency
the energy gets stored and passed back and forth between the capacitors,
like the swing going back and forth. This storage and energy swapping
emphasizes that frequency. Depending on the "Quality factor" or amount of
resonance that frequency can become much more apparent than the other
frequencies in the signal even if the input is wide-band.
When you are talking about delay and feedback, you are creating a digital
filter, but I think it is worthwhile to spend some time understanding the
theoretical concept and think in terms of energy and frequency. Your
feedback delay becomes the storage and certain frequencies will resonate
with that system.

Post by Mehdi Touzani
But it is having the resonance in parralel to a dry sound that bothers

me; but may be that's the only way to do ?
I'm not sure what you mean but I think you need some study in filter
design, because a single feedback delay causes comb filtering but its not a
classical lowpass. Is that what you are trying to achieve? Digital filters
are almost universally combinations of short delays (typically 1 sample)
placed in different patterns and fed back in different amounts (e.g.
https://en.wikipedia.org/wiki/Digital_filter#Filter_realization).
http://www.dspguide.com/ch14.htm
https://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/
VAFilterDesign_2.0.0a.pdf
That first one is a book that can help you more with the fundamentals in
the early chapters as well. I hope this is somewhat helpful, if not perhaps
I need to understand better specifically what you are trying to achieve.
_Spencer

Post by Mehdi Touzani
Hi all,
I follow the llist for a while, but I am not a DSP programmer, I do DSP
audio apps for about 20 years now, for sonic core plateform "Scope" and
Xite". I begin with other things like juce or flowstone, but so far,
scope is still far superior in terms of sound results. Too bad there is no
scripting tool for it (well there is but it is not available to me).
My question is probably weird for you - like super noob - , because i
am NOT looking for math or codes, but hints about a general
design/architecture.
So... how do you do a resonance in a lowpass circuit? :-) not the
math, not the code, just the architecture.
Personnally, i came to the conslusion that some kind of very short
delay with feedback, mixed in parallel with the non resonance low pass
sound, could do the trick. . The more feedback, the more resonance, and
with feedback over -6dB, it would begin to self resonate.
But it is having the resonance in parralel to a dry sound that bothers
me; but may be that's the only way to do ?
I have read about hardware filters and ok, there is math, but there is
also the effect of the hardware components. Some articles even suggest that
a bandpass in parralel could do the trick : or more exactly, a bandpass
fonction is created after the resonance, to remove frequencies that would
overlap with the cutoff.
So, any hints that could help me improve the process etc would be very
welcome.
Thanks
Mehdi
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https://lists.columbia.edu/mailman/listinfo/music-dsp

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[r***@web.de]

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[Stefan Sullivan]

Yes. The term helmholz resonator should be a hint ;) Basically when a
sounds gets added to itself after a delay you end up adding energy to the
frequency that corresponds to that delay amount. For very long echos we
don't hear it as a resonance, but for shorter delays it will boost higher
and higher frequencies into the audible range.

Stefan

Hello all
Is "feedback with delay" really resonance? I recognize many people
describe the effects of "room resonanes this way", but to my understanding
these are no resonances in the basic meaning but reflections. A resonance
is a self standing oscillating system like a guitar string or an air mass
in a Helmholtz resonator.
Rolf
*Gesendet:* Samstag, 21. Juli 2018 um 04:33 Uhr
*An:* "A discussion list for music-related DSP" <
*Betreff:* Re: [music-dsp] What is resonance?
Resonance is just delay with feedback. Resonance occurs when you delay a
signal and then feed it back with some gain to the input of the delay "in
phase"
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[Sound of L.A. Music and Audio]

A HHR performes both simple reflection and self oscillation. At the
beginning of the triggering phase the sound runs into it and is
reflected at the inner walls. A little part of the sound comes out
through the hole while a larger part is reflected creating steady waves
as known in all rooms as modes. These partly again come out. So far this
is just reflection.

But the little hole causes losses and local over pressure so it is also
an obstacle for the air inside which will start to pump. This way a
continous wave in beneath the HH-frequency is so to speak "loading" the
HHR which will become louder and louder. This causes a shift of the
phase difference between the incoming and outgoing waves coming to zero
finally when the feeding signal reaches the losses.

Therefore the HH might emphasize but also eliminate certain frequencies
in the room depending on the phase and volume difference and the length
of the signal. It might happen that a triggering sound is thus limited
and does not overload the room with modes but after the sound is over,
the HHR resonator will continue to feed the room with sound when
unloading his energy, unless damping material is used inside to limit this:

Loading Image...


A classical HHR built as a heavy iron sphere will have only one dominant
frequency and low losses, while a wooden case might have up to three. A
light wooden case might even pick up energy from the moving air inside
starting to emit sound on it's own resonance freqs.

So does the guitar: it picks up energy from the stings and performs both
energy storage in the wood and direct reflections inside the corpus. In
theory a guitar even has little HHR capabilites :-)

To distinguish both effects in the meaning of signal processing, one
could describe the reflections as a FIR behaviour while the energy
storing is an IIR. Real time simulation of loudspeaker cases can be done
this way, e.g. bass reflection tubes. In a very simple model the
reflections can also be replaced by IIR since the reflection of a sine
wave with a smoothed volume curve will also add to something like a II
response.

gtx

Dipl.-Ing. Jürgen Schuhmacher

Post by Stefan Sullivan
Yes. The term helmholz resonator should be a hint ;) Basically when a
sounds gets added to itself after a delay you end up adding energy to
the frequency that corresponds to that delay amount. For very long echos
we don't hear it as a resonance, but for shorter delays it will boost
higher and higher frequencies into the audible range.
Stefan
Hello all
Is "feedback with delay" really resonance? I recognize many people
describe the effects of "room resonanes this way", but to my
understanding these are no resonances in the basic meaning but
reflections. A resonance is a self standing oscillating system like
a guitar string or an air mass in a Helmholtz resonator.
 Rolf

[robert bristow-johnson]

I've been wondering about the connection that resonance and filter orders at least 2.  That's 2 delays (and feedback).
But if you're limiting the resonant frequencies to DC and Nyquist, then with a one-sample delay digital filter, you can have something like "resonance".
 Even if the single delay is two samples long (but no tap in the middle), that allows only DC, Nyquist, or half-Nyquist as tunable frequencies. 
So just sayin, in another sense of the word, that "resonance" can be had with a single *long* delay and one feedback path or with two arbitrarily short delays and two feedback paths.


--r b-j                     ***@audioimagination.com
"Imagination is more important than knowledge."




-------- Original message --------
From: Stefan Sullivan <***@gmail.com>
Date: 7/22/2018 2:20 PM (GMT-08:00)
To: A discussion list for music-related DSP <music-***@music.columbia.edu>
Subject: Re: [music-dsp] What is resonance?

Yes. The term helmholz resonator should be a hint ;) Basically when a sounds gets added to itself after a delay you end up adding energy to the frequency that corresponds to that delay amount. For very long echos we don't hear it as a resonance, but for shorter delays it will boost higher and higher frequencies into the audible range.
Stefan
On Sun, Jul 22, 2018, 08:10 <***@web.de> wrote:

Hello all

 

Is "feedback with delay" really resonance? I recognize many people describe the effects of "room resonanes this way", but to my understanding these are no resonances in the basic meaning but reflections. A resonance is a self standing oscillating system like a guitar string or an air mass in a Helmholtz resonator.

 

 Rolf

 

Gesendet: Samstag, 21. Juli 2018 um 04:33 Uhr

Von: "Andrew Simper" <***@cytomic.com>

An: "A discussion list for music-related DSP" <music-***@music.columbia.edu>

Cc: ***@lists.mcgill.ca, local-***@ccrma.stanford.edu, ***@music.vt.edu

Betreff: Re: [music-dsp] What is resonance?





Resonance is just delay with feedback. Resonance occurs when you delay a signal and then feed it back with some gain to the input of the delay "in phase"

 





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[charles morrow]

How about freezing and stretching moments. Is this resonance?

I've been wondering about the connection that resonance and filter orders at least 2. That's 2 delays (and feedback).
But if you're limiting the resonant frequencies to DC and Nyquist, then with a one-sample delay digital filter, you can have something like "resonance".
Even if the single delay is two samples long (but no tap in the middle), that allows only DC, Nyquist, or half-Nyquist as tunable frequencies.
So just sayin, in another sense of the word, that "resonance" can be had with a single *long* delay and one feedback path or with two arbitrarily short delays and two feedback paths.
--
"Imagination is more important than knowledge."
-------- Original message --------
Date: 7/22/2018 2:20 PM (GMT-08:00)
Subject: Re: [music-dsp] What is resonance?
Yes. The term helmholz resonator should be a hint ;) Basically when a sounds gets added to itself after a delay you end up adding energy to the frequency that corresponds to that delay amount. For very long echos we don't hear it as a resonance, but for shorter delays it will boost higher and higher frequencies into the audible range.
Stefan
Hello all
Is "feedback with delay" really resonance? I recognize many people describe the effects of "room resonanes this way", but to my understanding these are no resonances in the basic meaning but reflections. A resonance is a self standing oscillating system like a guitar string or an air mass in a Helmholtz resonator.
Rolf
Gesendet: Samstag, 21. Juli 2018 um 04:33 Uhr
Betreff: Re: [music-dsp] What is resonance?
Resonance is just delay with feedback. Resonance occurs when you delay a signal and then feed it back with some gain to the input of the delay "in phase"
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[Stefan Sullivan]

Oh interest challenge of the definition of resonance. The typical textbook
diagram shows a little local bump at some frequency in a bode diagram, but
if you consider dc the resonant frequency, then the only way to show a bump
is by being higher than all the other frequencies (i.e. monotonically
decreasing).

Hmm, I wonder. One common definition of resonance bandwidth is also the
"3dB" point. But I guess resonating at dc is probably not a common use case.

Stefan

Post by robert bristow-johnson
I've been wondering about the connection that resonance and filter orders
at least 2. That's 2 delays (and feedback).
But if you're limiting the resonant frequencies to DC and Nyquist, then
with a one-sample delay digital filter, you can have something like
"resonance".
Even if the single delay is two samples long (but no tap in the middle),
that allows only DC, Nyquist, or half-Nyquist as tunable frequencies.
So just sayin, in another sense of the word, that "resonance" can be had
with a single *long* delay and one feedback path or with two arbitrarily
short delays and two feedback paths.
--
"Imagination is more important than knowledge."
-------- Original message --------
Date: 7/22/2018 2:20 PM (GMT-08:00)
Subject: Re: [music-dsp] What is resonance?
Yes. The term helmholz resonator should be a hint ;) Basically when a
sounds gets added to itself after a delay you end up adding energy to the
frequency that corresponds to that delay amount. For very long echos we
don't hear it as a resonance, but for shorter delays it will boost higher
and higher frequencies into the audible range.
Stefan

Hello all
Is "feedback with delay" really resonance? I recognize many people
describe the effects of "room resonanes this way", but to my understanding
these are no resonances in the basic meaning but reflections. A resonance
is a self standing oscillating system like a guitar string or an air mass
in a Helmholtz resonator.
Rolf
*Gesendet:* Samstag, 21. Juli 2018 um 04:33 Uhr
*An:* "A discussion list for music-related DSP" <
*Betreff:* Re: [music-dsp] What is resonance?
Resonance is just delay with feedback. Resonance occurs when you delay a
signal and then feed it back with some gain to the input of the delay "in
phase"
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[robert bristow-johnson]

Any textbook study of resonant circuits and, using bilinear mapping a discrete-time counterpart, 3 dB bandwidths and Q is about a 2nd-order system.
A hemholtz resonator or a comb filter have resonance at many frequencies and they are much higher order tHan 2.  The are also tuned to harmonics.
The 2nd-order section, or "biquad" (with Q greater than 1/2) is resonant to only one non-negative frequency.
--r b-j                     ***@audioimagination.com
"Imagination is more important than knowledge."




-------- Original message --------
From: Stefan Sullivan <***@gmail.com>
Date: 7/22/2018 9:55 PM (GMT-08:00)
To: A discussion list for music-related DSP <music-***@music.columbia.edu>
Subject: Re: [music-dsp] What is resonance?

Oh interest challenge of the definition of resonance. The typical textbook diagram shows a little local bump at some frequency in a bode diagram, but if you consider dc the resonant frequency, then the only way to show a bump is by being higher than all the other frequencies (i.e. monotonically decreasing).
Hmm, I wonder. One common definition of resonance bandwidth is also the "3dB" point. But I guess resonating at dc is probably not a common use case.
Stefan

On Sun, Jul 22, 2018, 18:11 robert bristow-johnson <***@audioimagination.com> wrote:



I've been wondering about the connection that resonance and filter orders at least 2.  That's 2 delays (and feedback).
But if you're limiting the resonant frequencies to DC and Nyquist, then with a one-sample delay digital filter, you can have something like "resonance".
 Even if the single delay is two samples long (but no tap in the middle), that allows only DC, Nyquist, or half-Nyquist as tunable frequencies. 
So just sayin, in another sense of the word, that "resonance" can be had with a single *long* delay and one feedback path or with two arbitrarily short delays and two feedback paths.


--r b-j                     ***@audioimagination.com
"Imagination is more important than knowledge."




-------- Original message --------
From: Stefan Sullivan <***@gmail.com>
Date: 7/22/2018 2:20 PM (GMT-08:00)
To: A discussion list for music-related DSP <music-***@music.columbia.edu>
Subject: Re: [music-dsp] What is resonance?

Yes. The term helmholz resonator should be a hint ;) Basically when a sounds gets added to itself after a delay you end up adding energy to the frequency that corresponds to that delay amount. For very long echos we don't hear it as a resonance, but for shorter delays it will boost higher and higher frequencies into the audible range.
Stefan
On Sun, Jul 22, 2018, 08:10 <***@web.de> wrote:

Hello all

 

Is "feedback with delay" really resonance? I recognize many people describe the effects of "room resonanes this way", but to my understanding these are no resonances in the basic meaning but reflections. A resonance is a self standing oscillating system like a guitar string or an air mass in a Helmholtz resonator.

 

 Rolf

 

Gesendet: Samstag, 21. Juli 2018 um 04:33 Uhr

Von: "Andrew Simper" <***@cytomic.com>

An: "A discussion list for music-related DSP" <music-***@music.columbia.edu>

Cc: ***@lists.mcgill.ca, local-***@ccrma.stanford.edu, ***@music.vt.edu

Betreff: Re: [music-dsp] What is resonance?





Resonance is just delay with feedback. Resonance occurs when you delay a signal and then feed it back with some gain to the input of the delay "in phase"

 





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[David Reaves]

In the physical world, resonance can generally be observed as the frequency-dependent cyclic exchanging of energy between potential (stored) and kinetic (active) forms. A pendulum is a basic example: at either end of its swing a pendulum exhibits purely its maximal stored potential energy while momentarily there is zero (kinetic) motion; at mid-swing there is no storage (potential) and all energy is kinetic, in motion. Each form of energy has two opposing modes: potential has the two opposite extremes of the swing; kinetic, the two different directions of swing. The amplitudes of the two forms of energy are in quadrature, a 90° cyclic relationship; when charted, the two energy levels trace out sine and cosine forms.

In the real world, when continually given new energy with proper timing, a pendulum will swing indefinitely. If the outside source of energy is taken away, the resonance will decay: friction (resistance; damping) will slow and eventually stop the swinging. Within the limits of swing amplitude, the frequency of the pendulum's motion remains the same.

If you see such a back-and-forth, energy-trading relationship, there is likely resonance going on. Freezing can possibly be seen as energy storage and stretching can possibly be seen as activity, but unless one ‘feeds' the other and vice-versa, it’s probably not resonance.

(I will be pleased if someone corrects any false assumption I have made.)

David Reaves

Post by charles morrow
How about freezing and stretching moments. Is this resonance?

[Vadim Zavalishin]

Post by Mehdi Touzani
So... how do you do a resonance in a lowpass circuit? :-) not the
math, not the code, just the architecture.

There are many different ways to create resonance in a lowpass circuit
(esp. if the order is larger than 2). The higher is the order of the
filter, the more different answers there are.

Making a feedback loop around a lowpass chain is one way, but AFAIK it
works perfectly (or close to that) only for the 4th order filter (the so
called Moog ladder). I'm not aware of any standard generic structure (or
even a transfer function to begin with) which could be referred to as a
generic Nth order resonating filter. Recently I tried to propose one way
of generalizing the 2nd order resonance to an arbitrary order by what I
called "Butterworth filters of the 2nd kind", but this involves just the
transfer function, whereas you still have lots of freedom in the
implementation structure. You could look into the latest revision of my
book for more details (where I also explain the problems with the
lowpass feedback).

Regards,
Vadim