You are correct here.
It is the cone assembly including the voice coil which are coupled to the permanent magnetic field, which traderbam mentioned.
It doesn't, really.
But it is also pushed by the sound reflecting around inside the enclosure.
Yes.
It comes in when the physical movement in the system is converted back to electrical energy.
The resonant circuits you show are good for our purposes to approximate the behavior of a speaker driven by an amp. In fact, the circuit values of some of the elements should be changed if any element of the physical set-up is changed, like cabinet volume or damping material, for example. I am not trying to imply that the models do not work or anything like that.
On the topic of knowing what you're talking about, and in loose connection with the topic at hand:
Are step response and transient response different things?
My thinking is that a transient in the musical sense very rarely means the signal goes from zero to full amplitude in a microsecond. It's rather a question of an instrument (or several) suddenly striking a very loud note. That note would still consist of several sinusoidal ccomponents, wouldn't it?
If this is true, why would a transient be noticably harder to reproduce than the same spectrum played continously?
If the power bandwidth of the amplifier is sufficient (whatever that means...), the only thing I can think of is the power supply somehow not being instantly able to deliver the required power. As if more power requires a phone call to the power company, telling them to crank the generators.
Rune
Are step response and transient response different things?
My thinking is that a transient in the musical sense very rarely means the signal goes from zero to full amplitude in a microsecond. It's rather a question of an instrument (or several) suddenly striking a very loud note. That note would still consist of several sinusoidal ccomponents, wouldn't it?
If this is true, why would a transient be noticably harder to reproduce than the same spectrum played continously?
If the power bandwidth of the amplifier is sufficient (whatever that means...), the only thing I can think of is the power supply somehow not being instantly able to deliver the required power. As if more power requires a phone call to the power company, telling them to crank the generators.
Rune
sreten.
runebivrin said:
yes it would. And it stands to argue that physical instruments are less likely to produce a Dirac-like spike (you need infinite amount of force to move a mass suddenly, however small the mass is). so to produce an electronic step function, you need infinite bandwidth. But to produce anything less, you don't need infinite bandwidth.
The "first cycle distortion" is nothing but a gimic for marketing purposes, a problem created by those marketing types.
As an aside, try not to think of a step waveform as the same thing as a collection of harmonic sinusoids. It most certainly isn't. It is a step waveform.
Representing things as a sine series is just a mathematical convenience which works under special circumstances. Don't lose sight of reality.
Oh, I'm not sure it's just a marketing thing. As a software developer, I do recognize a general pattern. Once the audio designers of this world arrived at designs that were essentially distortion free (in the traditional sense), and with flat frequency response, it's rather unlikely there would be consensus, and all designers would stop improving their designs.
It's certainly turned in to a game of finding problems, such that they may then be solved.
I think this is what Graham is trying do do. Whether it will prove to be real is another issue, and if it's relevant to reproduction of audio is yet another - completely different - issue, and much harder to determine.
It would make sense that Graham can hear a difference, since he wants to hear it. I don't see the point in flogging him for that, but I also don't see the point in not realizing the dangers that lie in judging the results of your own efforts.
Rune
It's certainly turned in to a game of finding problems, such that they may then be solved.
I think this is what Graham is trying do do. Whether it will prove to be real is another issue, and if it's relevant to reproduction of audio is yet another - completely different - issue, and much harder to determine.
It would make sense that Graham can hear a difference, since he wants to hear it. I don't see the point in flogging him for that, but I also don't see the point in not realizing the dangers that lie in judging the results of your own efforts.
Rune
Could indeed be, but not necessarily. If a system is getting more transparent in one domain it might reveal problems in other ones that otherwise have been masked.
It is also clear that for a 100% accurate reproduction the WHOLE chain has to be able to reproduce from DC to infinity in terms of frequency response. And this is only one requirement out of many ! While the upper cutoff frequency of the amp should be quite high in order to not generate too much transient distortion one has to be aware that the real culprits in this respect are the speakers, microphones and storage media.
Regards
Charles
phase_accurate said:
Certainly. That's pretty much what I meant to say, with that added caveat that can be quite hard to find the problem that causes the unmasked artifacts. Several candidates may exist. You find a problem, solve it (you think), and analyze the results. Either way, you go on to uncover the next problem...
And the beat goes on, so to speak.
Rune
I added a simulation graph below, showing what happens when one passes a simulated sinusoid through an RC lowpass (green trace). I left away the original sinusoid for clarity. One can clearly see that there is something going on at beginning of the green trace. But that is simply due to the fact that the source signal is basically the same as the red trace shows: the product of a sinusoid and a step function. No one could reasonably assume that such a signal would be left untouched by a filter of ANY sort. But no one can assume such a signal to exist in reality either.
If one runs an FFT of the green trace from 0 to 1 ms then there is definitely a deviation from the spectrum of a pure sine to be seen (not in terms of harmonics but as a spectral envelope, due to the one-time character of the event). When transforming a subsequent full cycle, no distortion is present anymore (beware of the phase-shift).
So this definitely seems to be an artifact not present in the real world.
Regards
Charles
If one runs an FFT of the green trace from 0 to 1 ms then there is definitely a deviation from the spectrum of a pure sine to be seen (not in terms of harmonics but as a spectral envelope, due to the one-time character of the event). When transforming a subsequent full cycle, no distortion is present anymore (beware of the phase-shift).
So this definitely seems to be an artifact not present in the real world.
Regards
Charles
Attachments
traderbam said:
As an aside, try not to think of a step waveform as the same thing as a collection of harmonic sinusoids. It most certainly isn't. It is a step waveform.
Representing things as a sine series is just a mathematical convenience which works under special circumstances. Don't lose sight of reality.
Well, any PERIODIC wave form can be constructed (in reality, with real signals) from a certain number of sinussoids in the correct amplitude and phase relation ship. There is nothing artificial about that, it is reality.
What is not clear to me is whether a step function can be thought of as a periodic waveform. Maybe with an infinite long period? Anybody can shine light on this?
Jan Didden
traderbam said:As an aside, try not to think of a step waveform as the same thing as a collection of harmonic sinusoids. It most certainly isn't. It is a step waveform.
Representing things as a sine series is just a mathematical convenience which works under special circumstances. Don't lose sight of reality.
but even in the real world, if you were to feed all those harmonic sinusoids into a summing resistor network (or perfect speaker), you get a step function.
The real question is that can we humans hear those step functions, either directly or indirectly through a set of decomposed harmonic sinusoids.
For example, let's see a (less-then-perfect) step function can be decomposed into a set of harmonic sinusoids from DC - 1Mhz. And we will also produce an almost identical set ofo harmonic sinusoids from DC - 20Khz (or 30Khz, take your number).
when I feed those harmonics into a speaker, can a human reliably detect the difference between the two sets of harmonics? If she cannot, what does that mean for amp designers?
traderbam said:
I have in reality and on computers.
when I was in school, my professor did demonstrate the validity of FFT by suming increasing number of harmonics to show how the sum started to ressemble a step function.
You can also do this very easily in Matlab. and I am sure pretty much any spice program that has a sine function.
phase_accurate said:
But it is not a sinusoid at all. There is a sudden turn-on from the zero voltage (dv/dt = 0) to sinusoidal shape at the point of highest dv/dt (red line). Such a signal has wide frequency spectrum, just because of this turn-on. Nothing new that the beginning of the curve is smoothed by RC, depends only on this time constant. A question is whether a musical instrument can do something like this. The time shift between the two sinusoids is exactly equal to the time constant of the RC filter.
Let's nail once and for all the idea that this truncated single cycle of sine wave has anything to do with musical signals. I think there is a major misunderstanding going on between mathematicians and non-mathematicians here - see if this helps:
1. Imagine a physical object - a guitar string, a microphone diaphragm, a loudspeaker cone, your eardrum - trying to trace the this waveform. Up to time t=0, it is stationary; after time t=0 it is tracing the sine wave.
2. As soon as it starts tracing the sine wave, it begins moving with a particular velocity (dependent on the amplitude and frequency of the sine wave). Visually, imagine drawing a straight line touching the sine wave at t=0 and measuring its slope - this is its initial velocity.
3. In an instant, this object has changed from being stationary to moving with a given velocity. What is its acceleration - i.e. how quickly did its velocity change? It changed from nothing to something in no time at all: its acceleration must be infinite.
4. For the object to move, it must have a force acting on it equal to its mass times the acceleration. To produce infinite acceleration requires, therefore, infinite force.
Obviously, in the real world, you cannot generate an infinite force. The force which sets a guitar string moving has to come from the (finite) tension in the string; the force which moves a drum head is derived from the (finite) momentum of the drumstick. In other words:
No real physical signal ever looks exactly like Graham's single-cycle sine wave
What's more, the sort of limitations imposed by a finite force acting on an object of finite mass are exactly the same kind of limitations imposed by an amplifier of finite bandwidth; there is no justification for thinking the ear treats them differently.
Cheers
IH
1. Imagine a physical object - a guitar string, a microphone diaphragm, a loudspeaker cone, your eardrum - trying to trace the this waveform. Up to time t=0, it is stationary; after time t=0 it is tracing the sine wave.
2. As soon as it starts tracing the sine wave, it begins moving with a particular velocity (dependent on the amplitude and frequency of the sine wave). Visually, imagine drawing a straight line touching the sine wave at t=0 and measuring its slope - this is its initial velocity.
3. In an instant, this object has changed from being stationary to moving with a given velocity. What is its acceleration - i.e. how quickly did its velocity change? It changed from nothing to something in no time at all: its acceleration must be infinite.
4. For the object to move, it must have a force acting on it equal to its mass times the acceleration. To produce infinite acceleration requires, therefore, infinite force.
Obviously, in the real world, you cannot generate an infinite force. The force which sets a guitar string moving has to come from the (finite) tension in the string; the force which moves a drum head is derived from the (finite) momentum of the drumstick. In other words:
No real physical signal ever looks exactly like Graham's single-cycle sine wave
What's more, the sort of limitations imposed by a finite force acting on an object of finite mass are exactly the same kind of limitations imposed by an amplifier of finite bandwidth; there is no justification for thinking the ear treats them differently.
Cheers
IH
That's what I am desperately trying to explain all the time, but maybe I wasn't clear enough. It is the same sort of signal as the red trace shows, only difference being the point in time when it starts.
While musical instruments can generate spectral content that is reaching quite high in frequency, such a signal definitely doesn't exist in reality.
Regards
Charles