Hi,
does anyone know how to simulate the sound of an overdriven speaker? You know the crunchy sound when you torture it with a strong bass. It's nowhere near the sound of an normal overdrive with some kind of clipping.
Greetings
Thank you for your answer, but as I wrote I don't want the sound of simple clipping like clip~, tanh~ or overdrive~. I want the sound of a speaker crying for mercy because you put just too much through it.
But I don't know where to start. I know there are complex distortion effects, which are able to simulate different speaker cabinets after variable amps recorded by different microphones. But they all cost big money. Also I don't need the physical simulation. I just want the sound. If you want I can try to record the sound I'm talking about.
I tried to search for information how to do this but couldn't find anything usable. Not even an analysis what happens inside the speaker when you torture it like this.
I already know the forum but don't want to doublepost. I really liked the post about the oto biscuit. Neat distortion possibility's.
Am 15.10.2010 17:12, schrieb George Ker:
Hello, I can't really understand, so , you mean something different from
[clip~] ?
I' m sure you can find really good patches in the puredata.hurleur.com
forum searching about distortion , overdrive clip etc
GeorgeKer~
On 14 October 2010 23:19, - fallen_devil@gmx.de wrote:
Hi, does anyone know how to simulate the sound of an overdriven
speaker? You
know the crunchy sound when you torture it with a strong bass. It's nowhere near the sound of an normal overdrive with some kind of
clipping.
Greetings - _______________________________________________ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management ->
Hi!
I'm no speaker modeling expert at all, but I can try to describe what produces sounds in an overloaded speaker. There are various sources of distortion, symmetrical (mechanic suspension) and asymmetrical (magnetic field) and also time variant (temperature) and modulation (doppler effect / amplitude modulation) effects. I don't know which effects have a stronger or weaker influence, but I describe what I imagine:
High peak amplitude, positive wave:
speaker moves to the front, parts of the coil will not be in the magnetic field anymore. The field isn't zero outside the magnet gap, but I guess it decreases rapidly and is almost zero (so for example if half the coil is inside the magnet, the parts outside will not produce a force. So the force is only half as strong as it should. For simplicity you could say the field outside the magnet's gap is zero, so you have a linear function of excitation / current. Also If the coil moves out of the field its impedance will decrease which has influence on frequency response for higher frequencies a bit.
Heat
If the impedance is reduced as described above, a higher current will flow and heat the coil more than usual. The resistance of the coil will increase when it gets warmed and thus the efficiency of the speaker decreases (up to -7 dB I read somewhere, but this wasn't meant for almost dead speakers but heavy load). The heat needs some time to dissipate, so some kind of slow pumping compression effect occurs.
High amplitude, negative wave:
The speaker's coil might crash into the magnet and create different mechanical noises. Also the speakers diaphragm will be deformed by this crash and create various kinds of noise. Additionally it carries the noises the coil created - depending on the material and shape this sound different (paper, Kevlar, aluminum, etc sound different). If this crash doesn't occur (professional speakers don't have this issue usually) the negative wave will not be distorted too much and maybe distortion can be ignored.
In both directions the spider (basically a spring) starts to become nonlinear. Different manufacturers have different curves, but for small amplitudes they all pretend to be linear - so some experiments with sin~ or tanh~ might do it here.
Then generally there are happening doppler-effects on all speakers with big excursion. You could model them through a variable delay, modulated by a differentiated, low pass filtered signal (don't bite if I'm wrong, it's already very late... ). Amplitude modulation can be applied the same way (lowpass and apply it to higher frequencies).
so to sum it up:
apply symmetric distortion for the spider, split the path into positive and negative parts, for positive samples: tanh~, polynomials or other wave shapers, for negative parts let the signal untouched or add noises of a crashing coil (don't know how to achieve this), then sum both signals up, apply doppler effect, amplitude modulation and pumping compression. perhaps that sounds like your speakers then :)
I'm not sure if this works at all, but it definitely will sound very distorted in the end.
did you already discover http://www.klippel.de/pubs/papers.asp ?
cheers Martin
On 15.10.2010 21:10, - wrote:
Thank you for your answer, but as I wrote I don't want the sound of simple clipping like clip~, tanh~ or overdrive~. I want the sound of a speaker crying for mercy because you put just too much through it.
But I don't know where to start. I know there are complex distortion effects, which are able to simulate different speaker cabinets after variable amps recorded by different microphones. But they all cost big money. Also I don't need the physical simulation. I just want the sound. If you want I can try to record the sound I'm talking about.
I tried to search for information how to do this but couldn't find anything usable. Not even an analysis what happens inside the speaker when you torture it like this.
I already know the forum but don't want to doublepost. I really liked the post about the oto biscuit. Neat distortion possibility's.
Am 15.10.2010 17:12, schrieb George Ker:
Hello, I can't really understand, so , you mean something different from
[clip~] ?
I' m sure you can find really good patches in the puredata.hurleur.com
forum searching about distortion , overdrive clip etc
GeorgeKer~
On 14 October 2010 23:19, -fallen_devil@gmx.de wrote:
Hi, does anyone know how to simulate the sound of an overdrivenspeaker? You
know the crunchy sound when you torture it with a strong bass. It's nowhere near the sound of an normal overdrive with some kind ofclipping.
Greetings - _______________________________________________ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management ->http://lists.puredata.info/listinfo/pd-list
Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
On Sat, 16 Oct 2010, Martin Schied wrote:
field) and also time variant (temperature) and modulation (doppler effect / amplitude modulation) effects. I don't know which effects have a stronger or weaker influence,
for a sinewave, a peak of ±1 millimètre at 1 kiloHertz travels like
y = 0.001*sin(2000πt) mètres so dy/dt = 2π*cos(2000πt) mètres/seconde
so, the peak speed is ±2π m/s while the speed of sound is roughly 343 m/s, thus the doppler effect would be ±1.83 %, creating a vibrato of ±32 cents, but this vibrato is so fast, that it actually sounds like something else, because it runs at the same frequency as the input signal.
I tried it, and it sounds like related to waveshaping (although it's not). So maybe that's closer to what "fallen_devil" wants, because it has a quite richer sound than the usual [expr~ tanh($v1)].
I did it using [vd~]. (I imagine that I will soon retry with a natural spline version of it...)
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
This is getting interesting. I'm sorry, how did you do this with vd~?
2010/10/18 Mathieu Bouchard matju@artengine.ca
On Sat, 16 Oct 2010, Martin Schied wrote:
field) and also time variant (temperature) and modulation (doppler effect
/ amplitude modulation) effects. I don't know which effects have a stronger or weaker influence,
for a sinewave, a peak of ±1 millimètre at 1 kiloHertz travels like
y = 0.001*sin(2000πt) mètres so dy/dt = 2π*cos(2000πt) mètres/seconde
so, the peak speed is ±2π m/s while the speed of sound is roughly 343 m/s, thus the doppler effect would be ±1.83 %, creating a vibrato of ±32 cents, but this vibrato is so fast, that it actually sounds like something else, because it runs at the same frequency as the input signal.
I tried it, and it sounds like related to waveshaping (although it's not). So maybe that's closer to what "fallen_devil" wants, because it has a quite richer sound than the usual [expr~ tanh($v1)].
I did it using [vd~]. (I imagine that I will soon retry with a natural spline version of it...)
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC _______________________________________________ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
On Mon, 18 Oct 2010, Pierre Massat wrote:
This is getting interesting. I'm sorry, how did you do this with vd~?
C'est juste ça (en attachement). En fait, ma vraie patch est plus complexe, mais j'essaye pas vraiment de reproduire le phénomène physique de toute façon. Mes formules de vitesse sont même pas bonnes : il faudrait que j'utilise la loi de Maxwell et la loi de Hooke pour obtenir queqchose dans le domaine du réaliste, parce que y a rien qui dise comment les signaux audio de Pd peuvent correspondre à des millimètres dans cette patch ; J'imagine que ça me prendrait des [rpole~], [cpole~] et/ou [biquad~] quelque part là-dedans.
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
Sounds really cool with a guitar and with high gain (around 50). What's nice is the change in the spectrum depending on the volume of the input.
Le 18 octobre 2010 20:13, Mathieu Bouchard matju@artengine.ca a écrit :
On Mon, 18 Oct 2010, Pierre Massat wrote:
This is getting interesting. I'm sorry, how did you do this with vd~?
C'est juste ça (en attachement). En fait, ma vraie patch est plus complexe, mais j'essaye pas vraiment de reproduire le phénomène physique de toute façon. Mes formules de vitesse sont même pas bonnes : il faudrait que j'utilise la loi de Maxwell et la loi de Hooke pour obtenir queqchose dans le domaine du réaliste, parce que y a rien qui dise comment les signaux audio de Pd peuvent correspondre à des millimètres dans cette patch ; J'imagine que ça me prendrait des [rpole~], [cpole~] et/ou [biquad~] quelque part là-dedans.
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
On Mon, 18 Oct 2010, Pierre Massat wrote:
Sounds really cool with a guitar and with high gain (around 50). What's nice is the change in the spectrum depending on the volume of the input.
But all waveshapers also do change the spectrum according to the volume (except those that are linear, which basically means those waveshapers that are configured to do nothing.)
Perhaps you mean the manner in which this effect does the change of spectrum ?
I think that the sounds are often quite similar to what [expr~ sin($v1)] does, which is quite normal if the input data is rather sinusoïdal. Yet those are distinct formulæ that behave differently from each other in many cases.
Try various filters before [vd~] (but not affecting [delwrite~]). I mostly tried [rpole~], [lop~], [expr~ tanh($v1*$f2)]. Actually, I add them before I rescale the delay to the range 2<y<2+2n. (Be careful with hard clipping if you use things that have a gain, such as [rpole~] and obviously [*~]).
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
really nice distortion. I just fed it a few drum loops and it sounds very similar to drunken DJs at 5am...
I added a lop~ 200 before the modulation going into vd~ to reduce harsh sounds a bit, emphasizes the nice "pow" sound for bassdrums.
using the first deviation as modulation should be more physically correct but sounded very tinny and thin. Using direct signal for modulation like Mathieu used works very well and sounds more pleasant...
Interesting. I didn't expect it that way :)
cheers Martin
On Tue, 19 Oct 2010, Martin Schied wrote:
using the first deviation as modulation should be more physically correct but sounded very tinny and thin.
how do you compute that ?... how is the pressure wave supposed to relate to the digital wave ? I don't expect it to be a 1:1 mapping... my mechanics is a bit rusty. If [osc~ 1000] direct to [dac~] comes out as a ±1V peak potential, then what is [osc~ 2000] coming out as, and then how do you convert that to intensity (ampère) and power (watt), and then the kinetic energy it produces corresponds to which speed and ± peak distance ? (i remember that there's ½mv² somewhere in there... and there's réactance and impédance...)
Using direct signal for modulation like Mathieu used works very well and sounds more pleasant...
because I can't pretend to remember my grade 12 mechanics and grade 13 electricity so well, I concentrated on the æsthetics of it, but I'd be very curious about the physics of it. So, if you (or Martin Peach or other) can teach me a paragraph or two about this, I would be grateful.
Interesting. I didn't expect it that way :)
me neither, really. ;)
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
Hi!
Sorry for answering this late. And I was wrong in my last mail. The signal doesn't have to be differentiated but integrated (like you already did in your first post).?
The signal in pd represents the current flowing through the speaker's coil (if we assume it isn't capacitive or inductive load), producing an acceleration equivalent to the current on the speaker cone. The peak output voltage of the amplifier is equal for all frequencies and defines the maximum acceleration the cone can experience. So we can say the acceleration is
a(t)= a_max * -sin(w t) // w stands for omega = 2 * pi * f, a_max is the (peak) amplitude
If you want to know the speed you have to differentiate it by time:
v(t) = a_max * 1/w * cos(w t)
and for its travel:
x(t) = a_max 1/w² * sin(w t)
so the cone is moving faster for low frequencies (1/f) and also has more travel (1/f²).
It shouldn't be too hard to do this integration with basic pole / zero objects. A problem using integration only is the lack of mechanical damping. A real speaker goes back to x=0 if no signal is present. A simple integrator doesn't - so the 'simulated' cone would just fly away slowly. So some damping should be included in the integrator to make it stable. However I'm no expert on designing filters yet...
Looking at power and air pressure - we don't have to care about them as long as we don't want to include thermal effects or nonlinearities of the air I think. The pressure directly in front of the cone is related to the acceleration I think, but I'm not sure about that. Can anybody confirm that? I think that's not trivial to answer anyways, because already 10cm farther from the speaker the pressure and air velocity are different. The power from a 1 kHz sine and a 2 kHz sine are the same anyways, so why care...
cheers Martin
It shouldn't be too hard to do this integration with basic pole / zero objects. A problem using integration only is the lack of mechanical damping. A real speaker goes back to x=0 if no signal is present. A simple integrator doesn't - so the 'simulated' cone would just fly away slowly. So some damping should be included in the integrator to make it stable. However I'm no expert on designing filters yet...
[rpole~ 0.999] does it very well...
On Thu, 21 Oct 2010, Martin Schied wrote:
It shouldn't be too hard to do this integration with basic pole / zero objects. A problem using integration only is the lack of mechanical damping. A real speaker goes back to x=0 if no signal is present. A simple integrator doesn't
right. That's why you can't just use [rpole~ 1]. Then, any [rpole~] with a value between 0 and 1 will act as a convolution with an exponential decay function. An integral is a convolution with a constant function, such as exp(0*t).
Because the integral of the exponential decay function is bigger than 1, the result of [rpole~] will have some amount of gain.
- so the 'simulated' cone would just fly away slowly.
That's only in the case where the signal has a DC.
[rpole~ 0.999] does it very well...
Note that [rpole~] is dependent on sampling rate. So, assuming you have a sampling rate of 44100 Hz, the rate-independent way to do it is :
lop's gain compensation = 1 - 0.999 = 0.001 rpole's gain to compensate for = 1/0.001 = 1000 cutoff frequency = 0.001*44100/2π = 7.019 therefore use [lop~ 7.019] with [*~ 1000] (in any order)
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
Hi!
On 21.10.2010 07:17, Mathieu Bouchard wrote:
On Thu, 21 Oct 2010, Martin Schied wrote:
It shouldn't be too hard to do this integration with basic pole / zero objects. A problem using integration only is the lack of mechanical damping. A real speaker goes back to x=0 if no signal is present. A simple integrator doesn't
right. That's why you can't just use [rpole~ 1]. Then, any [rpole~] with a value between 0 and 1 will act as a convolution with an exponential decay function. An integral is a convolution with a constant function, such as exp(0*t).
nice way to look at it. I used the formulation y[n] = x[n]+ a[n] * y[n-1] in the help files and some semi-knowledge about filters...
Because the integral of the exponential decay function is bigger than 1, the result of [rpole~] will have some amount of gain.
- so the 'simulated' cone would just fly away slowly.
That's only in the case where the signal has a DC.
yeah, but this is often the case when messing things up in pd. I tried rpole~ 1 with sinewaves first which worked as integrator, but already had different results for the output of rpole~ if the wave started at 0 or pi/2 (which is logic, but I didn't think about it first...)
[rpole~ 0.999] does it very well...
Note that [rpole~] is dependent on sampling rate. So, assuming you have a sampling rate of 44100 Hz, the rate-independent way to do it is :
lop's gain compensation = 1 - 0.999 = 0.001 rpole's gain to compensate for = 1/0.001 = 1000 cutoff frequency = 0.001*44100/2π = 7.019 therefore use [lop~ 7.019] with [*~ 1000] (in any order)
I thought about lop~ doing similar things too, but didn't know what lop~ is doing and I'm sure I wouldn't have figured it out in any reasonable time this morning. thanks!
cheers Martin
On Fri, 22 Oct 2010, Martin Schied wrote:
yeah, but this is often the case when messing things up in pd. I tried rpole~ 1 with sinewaves first which worked as integrator, but already had different results for the output of rpole~ if the wave started at 0 or pi/2 (which is logic, but I didn't think about it first...)
um, yeah, the amount of DC is rather relative to where you start looking, and where you stop (or where you're at so far). That's why I used things like [rpole~ 0.99] to force it to recentre around 0 rather quickly.
lop's gain compensation = 1 - 0.999 = 0.001 rpole's gain to compensate for = 1/0.001 = 1000 cutoff frequency = 0.001*44100/2π = 7.019 therefore use [lop~ 7.019] with [*~ 1000] (in any order)I thought about lop~ doing similar things too, but didn't know what lop~ is doing and I'm sure I wouldn't have figured it out in any reasonable time this morning. thanks!
Ah, I also think that you'll like to know that the total weight of an input sample in [rpole~ a] can be written like this :
k = a^0 + a^1 + a^2 + a^3 + a^4 + ... but a*k = a^1 + a^2 + a^3 + a^4 + ... therefore k-a*k = a^0 = 1 k*(1-a) = 1 k = 1/(1-a) is how the gain of [rpole~] is computed above.
I attached my [lop2~] abstraction, which is a rpole~-version of [lop~], with a signal-rate right-inlet. I posted it some time ago.
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
On 22.10.2010 03:10, Mathieu Bouchard wrote:
On Fri, 22 Oct 2010, Martin Schied wrote:
yeah, but this is often the case when messing things up in pd. I tried rpole~ 1 with sinewaves first which worked as integrator, but already had different results for the output of rpole~ if the wave started at 0 or pi/2 (which is logic, but I didn't think about it first...)
um, yeah, the amount of DC is rather relative to where you start looking, and where you stop (or where you're at so far). That's why I used things like [rpole~ 0.99] to force it to recentre around 0 rather quickly.
I wanted to use a fairly high a < 1 because then the phase for all frequencies is approximately 90° off like for the ideal a=1. Using slightly smaller factors and comparing input / output didn't satisfy my expectations. maybe that would't matter at all - let's experiment...
lop's gain compensation = 1 - 0.999 = 0.001 rpole's gain to compensate for = 1/0.001 = 1000 cutoff frequency = 0.001*44100/2π = 7.019 therefore use [lop~ 7.019] with [*~ 1000] (in any order)I thought about lop~ doing similar things too, but didn't know what lop~ is doing and I'm sure I wouldn't have figured it out in any reasonable time this morning. thanks!
Ah, I also think that you'll like to know that the total weight of an input sample in [rpole~ a] can be written like this :
k = a^0 + a^1 + a^2 + a^3 + a^4 + ... but a*k = a^1 + a^2 + a^3 + a^4 + ... therefore k-a*k = a^0 = 1 k*(1-a) = 1 k = 1/(1-a) is how the gain of [rpole~] is computed above.
that's indeed interesting. So the gain is defined for a constant signal having the same input and output samples (or in other words DC having no amplification) if I understood it correctly.
I attached my [lop2~] abstraction, which is a rpole~-version of [lop~], with a signal-rate right-inlet. I posted it some time ago.
I remember it now, and already saved it in my mail archives :)
cheers Martin
On Fri, 22 Oct 2010, Martin Schied wrote:
I wanted to use a fairly high a < 1 because then the phase for all frequencies is approximately 90° off like for the ideal a=1. Using slightly smaller factors and comparing input / output didn't satisfy my expectations. maybe that would't matter at all - let's experiment...
How is the phase preservation an important thing for you ? I ask because I didn't really think of it as important... (and I still somewhat don't know when it's really important).
that's indeed interesting. So the gain is defined for a constant signal having the same input and output samples (or in other words DC having no amplification) if I understood it correctly.
It's defined for any signal. There are different equivalent ways to define the gain of a linear filter. In my head, I was thinking of an input signal containing a single 1 in a sea of zeroes... but it might be a bit easier to understand it using a constant input signal. Then for [sig~ 1], [rpole~ 1] will diverge (as much as the float32 number format can allow it to...) because 1/(1-1) is undefined (it's a division by zéro). But for [sig~ 1] again, [rpole~ 0.999] will output a constant 1000.
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
On 22.10.2010 06:05, Mathieu Bouchard wrote:
On Fri, 22 Oct 2010, Martin Schied wrote:
I wanted to use a fairly high a < 1 because then the phase for all frequencies is approximately 90° off like for the ideal a=1. Using slightly smaller factors and comparing input / output didn't satisfy my expectations. maybe that would't matter at all - let's experiment...
How is the phase preservation an important thing for you ? I ask because I didn't really think of it as important... (and I still somewhat don't know when it's really important).
I think it's not important for a speaker simulation either, but my assumption was that a correct behavior in phase would be a "sign" of a working integrator.
that's indeed interesting. So the gain is defined for a constant signal having the same input and output samples (or in other words DC having no amplification) if I understood it correctly.
It's defined for any signal. There are different equivalent ways to define the gain of a linear filter. In my head, I was thinking of an input signal containing a single 1 in a sea of zeroes... but it might be a bit easier to understand it using a constant input signal. Then for [sig~ 1], [rpole~ 1] will diverge (as much as the float32 number format can allow it to...) because 1/(1-1) is undefined (it's a division by zéro). But for [sig~ 1] again, [rpole~ 0.999] will output a constant 1000.
that's the way I understood it. fine!
Martin
On Thu, 21 Oct 2010, Martin Schied wrote:
The peak output voltage of the amplifier is equal for all frequencies and defines the maximum acceleration the cone can experience. So we can say the acceleration is
Alright, I should have thought about it. I mean, it's great that you wrote it, and it's what was necessary to get me to make a reasoning that would have been obvious if I were still in grade 13.
It shouldn't be too hard to do this integration with basic pole / zero objects. A problem using integration only is the lack of mechanical damping. A real speaker goes back to x=0 if no signal is present. A simple integrator doesn't - so the 'simulated' cone would just fly away slowly. So some damping should be included in the integrator to make it stable. However I'm no expert on designing filters yet...
A simple integrator has a pole at 1. With damping, you use any value a bit lower than 1. (But you found that already before I finished writing this mail)
Looking at power and air pressure - we don't have to care about them as long as we don't want to include thermal effects
Isn't the heat proportional to the mean power ? Then you just do [*~] with itself and then some kind of [rpole~] to account for the accumulation thereof. After that I don't really know what to do with that.
or nonlinearities of the air I think.
I don't know them at all. I've never heard of anyone taking them into account.
The pressure directly in front of the cone is related to the acceleration I think, but I'm not sure about that.
It has to : the speaker makes a sound by pushing and pulling on the air, and that changes the pressure.
Can anybody confirm that? I think that's not trivial to answer anyways, because already 10cm farther from the speaker the pressure and air velocity are different.
It has to... the reason why you hear the sound and why sound has a speed, is because neighbouring pressure differences cause pressure differences to propagate. It's a second-order differential equation, as the position of air particles is proportional to their acceleration. The Laplacian of the wave function along x,y,z is proportional to the 2nd derivative of the wave function along t... I'd write it like :
D[D[f,x],x] + D[D[f,y],y] + D[D[f,z],z] = D[D[f,t],t] / v²
Where v² is the square of the speed of sound.
With a slight coordinate change using imaginary numbers, you can see it as a Laplacian along x,y,z,t instead, in 4-dimensional spacetime, and the Laplacian is equal to zero. But that's only if the air is considered frictionless :)
The power from a 1 kHz sine and a 2 kHz sine are the same anyways, so why care...
Ah, that means that the mechanical amplitude (travel) of the wave is much smaller for treble than bass, is that right ?
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
Hi!
Looking at power and air pressure - we don't have to care about them as long as we don't want to include thermal effects
Isn't the heat proportional to the mean power ? Then you just do [*~] with itself and then some kind of [rpole~] to account for the accumulation thereof. After that I don't really know what to do with that.
one could feed the output of this [rpole~] into a [*~] to the input signal (or at any place later, but then it has to be cared for the delay of the doppler vd~ too, so better do it first). The exact parameters can be found by experiments, but as written in an earlier mail the signal reduction can be up to 7dB (I would use slightly more). I don't have time right now, but maybe I'll experiment later...
or nonlinearities of the air I think.
I don't know them at all. I've never heard of anyone taking them into account.
I think there aren't many too. The only case I can imagine and I heard of is for huge negative signals, where you can't go beyond 0 pascal of air pressure and the signal is clipped physically - but I doubt this ever happens in small speakers. Also I'm not sure if this only happens in compression speakers.
The pressure directly in front of the cone is related to the acceleration I think, but I'm not sure about that.
It has to : the speaker makes a sound by pushing and pulling on the air, and that changes the pressure.
yes, but it could also be seen in that way: the cone's travel compresses air in an enclosed volume. when the cone is at its travel peak (the acceleration is 0) the air is compressed at maximum. And I'm not sure if this is the case for a speaker in "free field" (not sure if that's the exact term) too. I know that there's something called radiation resistance - but I know nothing useful about it yet.
Can anybody confirm that? I think that's not trivial to answer anyways, because already 10cm farther from the speaker the pressure and air velocity are different.
It has to... the reason why you hear the sound and why sound has a speed, is because neighbouring pressure differences cause pressure differences to propagate. It's a second-order differential equation, as the position of air particles is proportional to their acceleration. The Laplacian of the wave function along x,y,z is proportional to the 2nd derivative of the wave function along t... I'd write it like :
D[D[f,x],x] + D[D[f,y],y] + D[D[f,z],z] = D[D[f,t],t] / v²
Where v² is the square of the speed of sound.
With a slight coordinate change using imaginary numbers, you can see it as a Laplacian along x,y,z,t instead, in 4-dimensional spacetime, and the Laplacian is equal to zero. But that's only if the air is considered frictionless :)
sorry, I don't understand that equation I think (I'm not understanding difference equations very well in general) and also I have no idea of Laplacians until now (I'll read about it and maybe understand later)
Ah, that means that the mechanical amplitude (travel) of the wave is much smaller for treble than bass, is that right ?
exactly.
cheers Martin
A perfect speaker will reproduce the sound exactly by transforming the instantaneous voltage to a displacement in or out. That's called 'compliance' in the speaker biz. The ideal speaker has zero mass and is totally rigid. So nonlinearities will show up: 1> when the speaker is massive and can't reach the ideal position quickly enough. 2> when the speaker deforms as it is accelerated from the centre but lags at the edges.
Also the stationary magnet is driving a coil in the speaker cone. When the speaker is overdriven the coil will be pushed away from the field of the magnet on the outward stroke and so the coil will be less able to move the speaker, so a kind of soft clipping will occur. But on the inward stroke the coil will bottom out and slam into the support structure, giving a hard clipping and possibly some bouncing.
I don't think the nonlinearities of the air are relevant here, or the doppler effect of the moving speaker.
Cavitation might occur with an underwater speaker, where bubbles are formed by the negative pressure on the trailing side of the cone.
Martin
On 2010-10-21 11:48, Martin Schied wrote:
Hi!
Looking at power and air pressure - we don't have to care about them as long as we don't want to include thermal effects
Isn't the heat proportional to the mean power ? Then you just do [*~] with itself and then some kind of [rpole~] to account for the accumulation thereof. After that I don't really know what to do with that.
one could feed the output of this [rpole~] into a [*~] to the input signal (or at any place later, but then it has to be cared for the delay of the doppler vd~ too, so better do it first). The exact parameters can be found by experiments, but as written in an earlier mail the signal reduction can be up to 7dB (I would use slightly more). I don't have time right now, but maybe I'll experiment later...
or nonlinearities of the air I think.
I don't know them at all. I've never heard of anyone taking them into account.
I think there aren't many too. The only case I can imagine and I heard of is for huge negative signals, where you can't go beyond 0 pascal of air pressure and the signal is clipped physically - but I doubt this ever happens in small speakers. Also I'm not sure if this only happens in compression speakers.
The pressure directly in front of the cone is related to the acceleration I think, but I'm not sure about that.
It has to : the speaker makes a sound by pushing and pulling on the air, and that changes the pressure.
yes, but it could also be seen in that way: the cone's travel compresses air in an enclosed volume. when the cone is at its travel peak (the acceleration is 0) the air is compressed at maximum. And I'm not sure if this is the case for a speaker in "free field" (not sure if that's the exact term) too. I know that there's something called radiation resistance - but I know nothing useful about it yet.
Can anybody confirm that? I think that's not trivial to answer anyways, because already 10cm farther from the speaker the pressure and air velocity are different.
It has to... the reason why you hear the sound and why sound has a speed, is because neighbouring pressure differences cause pressure differences to propagate. It's a second-order differential equation, as the position of air particles is proportional to their acceleration. The Laplacian of the wave function along x,y,z is proportional to the 2nd derivative of the wave function along t... I'd write it like :
D[D[f,x],x] + D[D[f,y],y] + D[D[f,z],z] = D[D[f,t],t] / v²
Where v² is the square of the speed of sound.
With a slight coordinate change using imaginary numbers, you can see it as a Laplacian along x,y,z,t instead, in 4-dimensional spacetime, and the Laplacian is equal to zero. But that's only if the air is considered frictionless :)
sorry, I don't understand that equation I think (I'm not understanding difference equations very well in general) and also I have no idea of Laplacians until now (I'll read about it and maybe understand later)
Ah, that means that the mechanical amplitude (travel) of the wave is much smaller for treble than bass, is that right ?
exactly.
cheers Martin
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Hi!
I agree with Martin Peach in most points and want to add some sentences.
On 22.10.2010 01:17, Martin Peach wrote:
A perfect speaker will reproduce the sound exactly by transforming the instantaneous voltage to a displacement in or out. That's called 'compliance' in the speaker biz. The ideal speaker has zero mass and is totally rigid. So nonlinearities will show up: 1> when the speaker is massive and can't reach the ideal position quickly enough.
this mainly filters the signal in a way of an analog lowpass filter and influences the intensity and phase spectra. It doesn't add new frequencies to it, so it's still called 'linear'. However throug the mass the system also has to deal with the stiffness and this causes some nonlinear effects.
2> when the speaker deforms as it is accelerated from the centre but lags at the edges.
I'm also sure these material nonlinearities will produce a main part of distortion frequencies in the spectrum. Especially when the speaker surround and spider are at their limits their imperfection will cause the whole cone to move 'sideways' and build up different modes. So this is definitely of interest for a (dying) speaker simulation. Probably this is one of the most challenging too...
Also the stationary magnet is driving a coil in the speaker cone. When the speaker is overdriven the coil will be pushed away from the field of the magnet on the outward stroke and so the coil will be less able to move the speaker, so a kind of soft clipping will occur. But on the inward stroke the coil will bottom out and slam into the support structure, giving a hard clipping and possibly some bouncing.
dependant on the construction of the speaker this slam will not occur, because the spider prevents this. (In most new speakers the spider is linear for small amplitudes and starts to become very hard and thus nonlinear at both ends. In a simulation one might want to chose if that slam (or i called it crash) happens or not. In a real speaker this often is really the death of the speaker because the coil is damaged permanently and then scratches on the magnet surface on every movement - I don't feel like I want to simulate these sounds :-\
I don't think the nonlinearities of the air are relevant here, or the doppler effect of the moving speaker.
I also agree that doppler effect is not the dominant parts of the distortions in a conventional speaker enclosure for music reproduction. Countermeasures are taken to reduce doppler effect as good as possible in these systems. In real speaker enclosements doppler effect is largely reduced by separating the audio spectrum on several speakers, so the bass speaker which does most of the movements only has to produce frequencies up to several hundreds of hertz. For example bass speakers in 3-ways systems are driven below 150 Hz in most cases - doppler effect becomes very low in this spectrum and mid range speaker have almost no visible travel anymore. However the doppler effect occurs in every speaker with moving parts and especially for full range speakers this becomes important. Guitar amps often use bass drivers in full range, so this has some practical relevance for musicians too.
I'd be interested what kind of speakers fallen_devil was interested in when originally posting his question to the list. Also a record of the noise would be nice for comparison...
cheers Martin
On Thu, 21 Oct 2010, Martin Schied wrote:
Isn't the heat proportional to the mean power ? Then you just do [*~] with itself and then some kind of [rpole~] to account for the accumulation thereof. After that I don't really know what to do with that.one could feed the output of this [rpole~] into a [*~] to the input signal (or at any place later, but then it has to be cared for the delay of the doppler vd~ too, so better do it first).
Why would you be doing the doppler first ? The heat is generated first, in the moving coil, but the doppler is relative to the observer, who comes at the very end in the data flow from the amp to the ear. Thus it seems to me that the [vd~] should come at the very end.
How does one take the réactance into account, again ?... then we'd have to change the first [*~] to account for ampères not following volts, and do we have to change the other [*~] too ?
I think there aren't many too. The only case I can imagine and I heard of is for huge negative signals, where you can't go beyond 0 pascal of air pressure and the signal is clipped physically - but I doubt this ever happens in small speakers. Also I'm not sure if this only happens in compression speakers.
I doubt that it (getting close to 0 pascal) happens at all. It sounds more like a weapon of mass destruction, than like something for listening to.
Though... in some ways, it does happens, at a very small scale. What's the speed of air molecules, and how much time do they take to fill the void made by the speaker moving ? What happens if the speaker moves faster than that ?... (and is that actually the Doppler effect said using different words ?)
It has to : the speaker makes a sound by pushing and pulling on the air, and that changes the pressure.
To be clear, by pulling I just mean the apparent pulling that happens when air randomly expands to fill the void introduced by the speaker... it's this «pulling» that I'm talking about now.
yes, but it could also be seen in that way: the cone's travel compresses air in an enclosed volume. when the cone is at its travel peak (the acceleration is 0) the air is compressed at maximum. And I'm not sure if this is the case for a speaker in "free field" (not sure if that's the exact term) too. I know that there's something called radiation resistance - but I know nothing useful about it yet.
I don't know what you mean here by «enclosed volume», «free field», nor «radiation resistance».
sorry, I don't understand that equation I think (I'm not understanding difference equations very well in general) and also I have no idea of Laplacians until now (I'll read about it and maybe understand later)
I just mean that if you make a map of the pressure in x,y,z and t, you will find that normal wave transmission means that the sum of the 3 second spatial derivatives is proportional to the second temporal derivative. This can also apply if you remove the z and also if you remove the y, so perhaps it's easiest for you to first see that it works with just x and t.
The notation D[f,t] means something like df/dt but I don't have the partial derivative symbol nor the other funny notations used in math texts (indices, multiple-level division).
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC
Hi Mathieu -
again, sorry for the big delay. I was a bit busy the past 2 weeks.
On 22.10.2010 07:35, Mathieu Bouchard wrote:
On Thu, 21 Oct 2010, Martin Schied wrote:
Isn't the heat proportional to the mean power ? Then you justdo [*~] with itself and then some kind of [rpole~] to account for the accumulation thereof. After that I don't really know what to do with that.
one could feed the output of this [rpole~] into a [*~] to the input signal (or at any place later, but then it has to be cared for the delay of the doppler vd~ too, so better do it first).
Why would you be doing the doppler first ? The heat is generated first, in the moving coil, but the doppler is relative to the observer, who comes at the very end in the data flow from the amp to the ear. Thus it seems to me that the [vd~] should come at the very end.
yes, absolutely...
How does one take the réactance into account, again ?... then we'd have to change the first [*~] to account for ampÚres not following volts, and do we have to change the other [*~] too ?
I think there are 2 main factors where reactance is important. The first is the varying current flow for heat, the second is the varying frequency response of the speaker. However I'm not knowing of a possibility to model the circuit so you actually have a current and a voltage signal. To calculate the heat production the voltage isn't used. You have to know the resistance of the coil and the current flowing through it. And since the force on the cone relates on the current flow (and this is what we hear) and not the voltage we should just not care about the voltage and assume the signal in pd is the current signal. Or expressed in other words the system should be treated like no difference in current and voltage can happen. At least it seems to me this makes a lot of things easier and the audibe effects could be estimated. At least for me a realistic modeling with verification is out of my knowlegde and also my time capabilities are limited at the moment...
I think there aren't many too. The only case I can imagine and I heard of is for huge negative signals, where you can't go beyond 0 pascal of air pressure and the signal is clipped physically - but I doubt this ever happens in small speakers. Also I'm not sure if this only happens in compression speakers.
I doubt that it (getting close to 0 pascal) happens at all. It sounds more like a weapon of mass destruction, than like something for listening to.
Though... in some ways, it does happens, at a very small scale. What's the speed of air molecules, and how much time do they take to fill the void made by the speaker moving ? What happens if the speaker moves faster than that ?... (and is that actually the Doppler effect said using different words ?)
That's beyond my knowledge, but I think that's not the point. If you calculate the maximum pressure before the negative peak is zero you have an spl of approximately 135dB which is not that much for pressure levels directly in front of a speaker - possibly I calculated it wrong? I used: air pressure: 101.325 Pa and /p/_0 = 20 µPa RMS, which gave me 134.09 dB (for a wave with RMS of 101.325 Pa - so ideally I would have to take this as peak level but that doesn't change much, only factor sqrt(2)).
I don't know what you mean here by «enclosed volume», «free field», nor «radiation resistance».
radiation resistance is the same like impedance, but for mechanical systems. You can treat the spring/mass system of the speaker and the air similar to an electrical circuit driving an antenna as far as I understood. And similar to electrical load you can have pure reactance and pure resistance. Unfortunately the internet isn't very wise concerning acoustics and speaker systems and is full of voodoo and homeopathy instead using the same vocabulary, so I could not find very much about it on a quick search.
By enclosed volume I thought of an air tight wooden box with no holes other than that for the speaker in it - just like most older conventional speakers. Pressing the membrane into the box creates a pressure proportional to the excitation of the cone and not anymore to the acceleration. I think this closed volume would be called a high radiation resistance, because the pressure (analog to the voltage) is high for very small air flow (analog to the current).
Martin
Hello,
sorry for being away from my own topic. Somewhere I decided to first find my own way and then look into what you wrote. Which now opens up a new bunch of ideas.
In the attachment you can take a look at what I produced so far (pd-extended). It is not finished and I think some sliders could be thrown out. It was more an intuitive approach and not a physical model. The result seems to be noisy enough for me and has some interesting effects and uses in it. Not that it is near any speaker simulation like you discussed here. The -old version was the first draft. But the heavy use of fexpr~ made my CPU cry. My current version uses one block delays and tries to be the same. But the result is quiet different, as the 64 samples delay makes it impossible to cut the waveform like in the -old version. But I reduced CPU usage to 1/5th, which is still too much for my liking.
By the way it is kind of sad that everyone (including me) always uses tanh, while there are much much more functions out there which could be better suited, produce less high harmonics (aliasing!) or just sound better. A while ago I took a small dive into this topic but only remember some sigmoid functions, but not what their effect was: atan, 1/(1+exp), x/sqrt(x^2), [sqare-law], erf() [I couldn't test because its only in the documentation of expr but not useable] But this should be a topic of its own.
@Martin Thank you for the complex and interesting physical analyzation. Now I have a bunch of new ideas of what I could do next. No I didn't know that page but it looks interesting. I'll soon take a closer look at it.
I'd be interested what kind of speakers fallen_devil was interested in when originally posting his question to the list. Also a record of the noise would be nice for comparison...
I am interested in the whole topic and the possibility to create completely different sounds. Not the sound of one special speaker. I wanted to do a record too, maybe I get around to it soon. But I'm not sure what I should use as a test sample. I thought about increasingly loud snare + bassdrum and a bassynth. Any other suggestion?
@Mathieu Great distortion you created there. Also a topic of its own. Thanks for the lop2~ now I don't have to always use the iemlib filters.
Greetings
Am 16.10.2010 06:46, schrieb Martin Schied:
Hi!
I'm no speaker modeling expert at all, but I can try to describe what produces sounds in an overloaded speaker. There are various sources of distortion, symmetrical (mechanic suspension) and asymmetrical (magnetic field) and also time variant (temperature) and modulation (doppler effect / amplitude modulation) effects. I don't know which effects have a stronger or weaker influence, but I describe what I imagine:
High peak amplitude, positive wave:
speaker moves to the front, parts of the coil will not be in the magnetic field anymore. The field isn't zero outside the magnet gap, but I guess it decreases rapidly and is almost zero (so for example if half the coil is inside the magnet, the parts outside will not produce a force. So the force is only half as strong as it should. For simplicity you could say the field outside the magnet's gap is zero, so you have a linear function of excitation / current. Also If the coil moves out of the field its impedance will decrease which has influence on frequency response for higher frequencies a bit.
Heat
If the impedance is reduced as described above, a higher current will flow and heat the coil more than usual. The resistance of the coil will increase when it gets warmed and thus the efficiency of the speaker decreases (up to -7 dB I read somewhere, but this wasn't meant for almost dead speakers but heavy load). The heat needs some time to dissipate, so some kind of slow pumping compression effect occurs.
High amplitude, negative wave:
The speaker's coil might crash into the magnet and create different mechanical noises. Also the speakers diaphragm will be deformed by this crash and create various kinds of noise. Additionally it carries the noises the coil created - depending on the material and shape this sound different (paper, Kevlar, aluminum, etc sound different). If this crash doesn't occur (professional speakers don't have this issue usually) the negative wave will not be distorted too much and maybe distortion can be ignored.
In both directions the spider (basically a spring) starts to become nonlinear. Different manufacturers have different curves, but for small amplitudes they all pretend to be linear - so some experiments with sin~ or tanh~ might do it here.
Then generally there are happening doppler-effects on all speakers with big excursion. You could model them through a variable delay, modulated by a differentiated, low pass filtered signal (don't bite if I'm wrong, it's already very late... ). Amplitude modulation can be applied the same way (lowpass and apply it to higher frequencies).
so to sum it up:
apply symmetric distortion for the spider, split the path into positive and negative parts, for positive samples: tanh~, polynomials or other wave shapers, for negative parts let the signal untouched or add noises of a crashing coil (don't know how to achieve this), then sum both signals up, apply doppler effect, amplitude modulation and pumping compression. perhaps that sounds like your speakers then :)
I'm not sure if this works at all, but it definitely will sound very distorted in the end.
did you already discover http://www.klippel.de/pubs/papers.asp ?
cheers Martin
On 15.10.2010 21:10, - wrote:
Thank you for your answer, but as I wrote I don't want the sound of simple clipping like clip~, tanh~ or overdrive~. I want the sound of a speaker crying for mercy because you put just too much through it.
But I don't know where to start. I know there are complex distortion effects, which are able to simulate different speaker cabinets after variable amps recorded by different microphones. But they all cost big money. Also I don't need the physical simulation. I just want the sound. If you want I can try to record the sound I'm talking about.
I tried to search for information how to do this but couldn't find anything usable. Not even an analysis what happens inside the speaker when you torture it like this.
I already know the forum but don't want to doublepost. I really liked the post about the oto biscuit. Neat distortion possibility's.
Am 15.10.2010 17:12, schrieb George Ker:
Hello, I can't really understand, so , you mean something different from
[clip~] ?
I' m sure you can find really good patches in the puredata.hurleur.com
forum searching about distortion , overdrive clip etc
GeorgeKer~
On 14 October 2010 23:19, - fallen_devil@gmx.de wrote:
Hi, does anyone know how to simulate the sound of an overdrivenspeaker? You
know the crunchy sound when you torture it with a strong bass. It's nowhere near the sound of an normal overdrive with some kind ofclipping.
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On Wed, 10 Nov 2010, - wrote:
By the way it is kind of sad that everyone (including me) always uses tanh, while there are much much more functions out there which could be better suited, produce less high harmonics (aliasing!) or just sound better. A while ago I took a small dive into this topic but only remember some sigmoid functions, but not what their effect was: atan, 1/(1+exp),
1/(1+exp) is the same as tanh, except for the input gain, output gain, and output dc.
x/sqrt(x^2),
That's the same as x/abs(x), which is the limit of tanh as input gain goes towards infinity. It's the same as [>~] except when the input is exactly zero, and except for the output gain and output dc.
[sqare-law],
What's this ?
erf() [I couldn't test because its only in the documentation of expr but not useable] But this should be a topic of its own.
Sorry, but [expr erf($f1)] does work. There are functions in [expr]'s docs that don't really exist in expr, but erf is not one of them.
| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
Hi the papers on http://www.klippel.de/pubs/papers.asp where quiet interesting. But the page went down. It looks like it went to: http://www.klippel.de/nc/know-how/literature/papers.html?sword_list%5B0%5D=p...
Greetings
Am 16.10.2010 06:46, schrieb Martin Schied:
Hi!
I'm no speaker modeling expert at all, but I can try to describe what produces sounds in an overloaded speaker. There are various sources of distortion, symmetrical (mechanic suspension) and asymmetrical (magnetic field) and also time variant (temperature) and modulation (doppler effect / amplitude modulation) effects. I don't know which effects have a stronger or weaker influence, but I describe what I imagine:
High peak amplitude, positive wave:
speaker moves to the front, parts of the coil will not be in the magnetic field anymore. The field isn't zero outside the magnet gap, but I guess it decreases rapidly and is almost zero (so for example if half the coil is inside the magnet, the parts outside will not produce a force. So the force is only half as strong as it should. For simplicity you could say the field outside the magnet's gap is zero, so you have a linear function of excitation / current. Also If the coil moves out of the field its impedance will decrease which has influence on frequency response for higher frequencies a bit.
Heat
If the impedance is reduced as described above, a higher current will flow and heat the coil more than usual. The resistance of the coil will increase when it gets warmed and thus the efficiency of the speaker decreases (up to -7 dB I read somewhere, but this wasn't meant for almost dead speakers but heavy load). The heat needs some time to dissipate, so some kind of slow pumping compression effect occurs.
High amplitude, negative wave:
The speaker's coil might crash into the magnet and create different mechanical noises. Also the speakers diaphragm will be deformed by this crash and create various kinds of noise. Additionally it carries the noises the coil created - depending on the material and shape this sound different (paper, Kevlar, aluminum, etc sound different). If this crash doesn't occur (professional speakers don't have this issue usually) the negative wave will not be distorted too much and maybe distortion can be ignored.
In both directions the spider (basically a spring) starts to become nonlinear. Different manufacturers have different curves, but for small amplitudes they all pretend to be linear - so some experiments with sin~ or tanh~ might do it here.
Then generally there are happening doppler-effects on all speakers with big excursion. You could model them through a variable delay, modulated by a differentiated, low pass filtered signal (don't bite if I'm wrong, it's already very late... ). Amplitude modulation can be applied the same way (lowpass and apply it to higher frequencies).
so to sum it up:
apply symmetric distortion for the spider, split the path into positive and negative parts, for positive samples: tanh~, polynomials or other wave shapers, for negative parts let the signal untouched or add noises of a crashing coil (don't know how to achieve this), then sum both signals up, apply doppler effect, amplitude modulation and pumping compression. perhaps that sounds like your speakers then :)
I'm not sure if this works at all, but it definitely will sound very distorted in the end.
did you already discover http://www.klippel.de/pubs/papers.asp ?
cheers Martin
On 15.10.2010 21:10, - wrote:
Thank you for your answer, but as I wrote I don't want the sound of simple clipping like clip~, tanh~ or overdrive~. I want the sound of a speaker crying for mercy because you put just too much through it.
But I don't know where to start. I know there are complex distortion effects, which are able to simulate different speaker cabinets after variable amps recorded by different microphones. But they all cost big money. Also I don't need the physical simulation. I just want the sound. If you want I can try to record the sound I'm talking about.
I tried to search for information how to do this but couldn't find anything usable. Not even an analysis what happens inside the speaker when you torture it like this.
I already know the forum but don't want to doublepost. I really liked the post about the oto biscuit. Neat distortion possibility's.
Am 15.10.2010 17:12, schrieb George Ker:
Hello, I can't really understand, so , you mean something different from
[clip~] ?
I' m sure you can find really good patches in the puredata.hurleur.com
forum searching about distortion , overdrive clip etc
GeorgeKer~
On 14 October 2010 23:19, - fallen_devil@gmx.de mailto:fallen_devil@gmx.de wrote:
Hi, does anyone know how to simulate the sound of an overdrivenspeaker? You
know the crunchy sound when you torture it with a strong bass. It's nowhere near the sound of an normal overdrive with some kind ofclipping.
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