PMA said:
Not quite sure if you agree or disagree with what I meant. What I meant was that when transients are discussed, they are often equated with step responses. That's certainly one way of looking at it, but such signals are rarely a part of music. I don't know of a real instrument that could produce such signals. And even if it existed, after passing through a CD with its associated filtering, would it still be there?
A musical transient is just a sudden crescendo, and as such unlikely to be a special case for an amplifier.
Rune
Though a step is a theoretical signal it can be used to test transient accuracy. I by myself do not except any sound system to accurately reproduce a step. Far from that. But there are some reasonable limits whithin those the response should lie. An amp with an upper cutoff frequency of 150 to 200 kHz and no overshoots is fully satisfying my taste since other parts of the system are much more constrained.
Regards
Charles
Regards
Charles
It sounds like you're keen on proving that the fourier transform is a farce... Just so you know, you're going against decades and decades of real world experience in hundreds of scientific, mathematic and engineering fields.traderbam said:
I'm sure that this has been stated, but here's how things work:
(1) Any steady state waveform can be modelled as a sum of sinusoids. Even a square wave can be created from sinusoids; the only condition is that an infinite number of sinusoids approaching infinite frequency is required to produce a "perfect" square wave.
And real world experience supports fourier theory; for example, if you trim off the higher frequencies of a square wave using a low pass filter (or an amplifier with a finite bandwidth, or so forth) then the square wave will look more and more like a sine wave as the cutoff frequency is lowered.
(2) Any non-steady-state waveform can be modelled as an amplitude modulated signal. In a simple case, a fading tone can consist of a downward ramp (modelled out of sinusoids) multiplied by a fading tone (a sinusoid) which causes heterodyning in the frequency domain. Or you can multiply together an audio signal and a high frequency sinusoid and amplify the output power to tens of kilowatts and create an AM radio transmitter.
(3) The statement in (2) allows you to model a transient using fourier series. Your "first cycle distortion" waveform consists of a step response multiplied by a sin() function - essentially, a modulated step response. The frequency components of such a signal are very easily calculated.
Since a step response has infinite frequency components, so will the "first cycle distortion" signal.
The only thing is, THESE SIGNALS DON'T EXIST IN THE REAL WORLD! To reproduce such a signal perfectly, the following conditions have to exist:
- Using a "guitar player" example, the guitar player will have to pluck a string with zero inertia. After the pick leaves the string, the tension introduced on the string by bending it with the pick combined with the natural tension on the string will cause the string to begin accelerating towards the "zero" position - It will *not* suddenly "snap" from zero to high velocity as depicted in the FCD waveform; this requires infinite acceleration. Since F=M*A, for such a condition to exist the string would either have to be hit with an infinite amount of force (which isn't true; only the string's tension is accelerating it) or the string will require zero mass... come to think of it, wouldn't a guitar string with zero mass oscillate at infinite frequency?
- A cymbal strike is probably a better example; a cymbal hit hard with a drum stick will accelerate much faster than a guitar string. The same thing applies though; the mass of the cymbal combined with the ductility of the drum stick's wood and cymbal's metal will limit the acceleration of the cymbal.
But assuming that a diamond cymbal was hit by a kryptonite drum stick and the cymbal had instantaneous velocity (eg, FCD waveform) then the air in the room would then have to instantly accelerate (which it can't, it has mass and compressibility), the recording microphone's element would have to move instantly (same thing), and finally the recording medium would have to carry such a signal. CD's have a nyquist limit, and LPs have a frequency limit imposed by the mass of the stylus.
Anyhow, I think I've typed more than enough
My job involves doing quite a lot of fourier stuff too (i'm an engineer at a radio broadcasting equipment company)traderbam said:
I've also got a physics background. The point of my post was to say that creating an "instant-on-sine-wave" is impossible for two reasons - (1) fourier theory says that such a signal has infinite frequency components, which you can't have in the real world, and (2) an "instant-on-sine-wave" signal cannot come from any sort of mechanical instrument, since some component inside would have to undergo infinite acceleration, which is not possible. And such a signal cannot be recorded for the same reasons.
"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."
"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."
And if we are talking about a recording of a live musical event the mass (strings, diaphrams etc, PLUS air) being moved is far from arbitrarily small. Pure computer generated electronic music may be another matter as you could concievably create a file where the data at word #1 has minumum value and at word #2 has the max. It's still not instantaneous but limited only by contraints of sampling requency and word length.
And if we are talking about a recording of a live musical event the mass (strings, diaphrams etc, PLUS air) being moved is far from arbitrarily small. Pure computer generated electronic music may be another matter as you could concievably create a file where the data at word #1 has minumum value and at word #2 has the max. It's still not instantaneous but limited only by contraints of sampling requency and word length.
subwo1 said:
But all of those elements are passive. Not active. The only active elements involved here are the tubes and/or transistors in the amplifier. Everything else is either resistive or reactive.
But that's ultimately just energy being returned to the system. Not from an external energy source.
You mean like how the collapsing magnetic field around an inductor is being converted back to electrical energy?
Which takes me back to my previous question. How is it exactly that a speaker is an AC generator but an inductor isn't?
se
Whether the sinusoidals comprising an FFT "exist" in the real world or not is just part of a broader question of relating a "real" phemonon to it's model. The question exists with regard to anything physical that is described by a model or equation. As a famous example, recall that Einstein never really could accept the probabalistic aspects of quantum theory even though he was the developer of the theory. You can also expect that if string theory is successful, the next century or so will filled with tortuous debates about whether the universe in really constructed of multidimentional strings or if that is just a useful mathematical tool.
I'm inclined to think that the question in it's various forms is just a koan. Something to think about when there is nothing better to do.
I'm inclined to think that the question in it's various forms is just a koan. Something to think about when there is nothing better to do.
By that definition a speaker isn't "active". But it does rely on a permanent magnet which is an "external" field source as opposed to an external voltage source as it were.
In any case I think your questions are about what the differences are between motors, ac generators and inductors. They aren't really different at all. They all rely on Faraday's Laws (with some Ampere thrown in) which connect magnetic fields, current flows and mechanical forces. These effects are bi-directional so a speaker is also a microphone and vise-versa. A speaker is both a motor and a generator and is so at the same time, regardless of whether an amplifier is driving it or not.
It is sort of splitting hairs to try to define how much cone movement is due to the intended amp signal and how much is due to airborn reflections or even someone tapping on the cone with their finger. Everything is bidirectional. But quite unlike a simple inductor a speaker presents complex resonances and real time delays due to the speed of sound in air.
In any case I think your questions are about what the differences are between motors, ac generators and inductors. They aren't really different at all. They all rely on Faraday's Laws (with some Ampere thrown in) which connect magnetic fields, current flows and mechanical forces. These effects are bi-directional so a speaker is also a microphone and vise-versa. A speaker is both a motor and a generator and is so at the same time, regardless of whether an amplifier is driving it or not.
It is sort of splitting hairs to try to define how much cone movement is due to the intended amp signal and how much is due to airborn reflections or even someone tapping on the cone with their finger. Everything is bidirectional. But quite unlike a simple inductor a speaker presents complex resonances and real time delays due to the speed of sound in air.
runebivrin said:
I couldn't agree less.
Amplifier design still has real problems that need quantifying and addressing.
GM aural observations I've no qualms with at all.
There are very good reasons why the amplifier designs he favours
sound the way they do, and I'm not questioning aural quality, they
are good sounding amplifiers.
What is dubious is GM attitude as to why they sound that way.
His technical approach cannot be called rigorous.
Despite all the debate here I maintain his FCD is just another
way of observing technical parameters already well understood.
sreten.
