[opnly bafld]

Before Daryl gets all excited about this statement don't forget that there are actually two things being discussed here: the time/frequency domain representations of a signal and the time/frequency domain response of a system.

Come on John, I happen to have an amp that has very good synergy all by its self.

Lin

[opaqueice]

Exactly!  What had been stated earlier was that FR and time domain are simply different views of the same thing.  To me, they're complementary and to be viewed together as you stated.  FR by itself cannot determine time domain issues.

Well, sometimes it's nicer to talk about frequency domain information which includes not just the amplitude (which is probably what people usually mean when they say frequency response) but also the phase.  In mathematical terms, when you take a Fourier transform of the (real) time-domain signal you get a complex function of frequency.  The phase of that complex number, as a function of frequency, tells you about the phase response, and the amplitude tells you about the frequency response.

That frequency information really is simply a different but equivalent view of the time domain, as Daryl has emphasized, but you need both the amplitude and the phase.  It might be worth noting that our ears are really, really bad at hearing phase differences in real sounds.  However it's easy to generate artificial tones where phase distortions are audible.

No, because that assumes that the system is linear, which (since we are talking about distortion) it isn't.

I think if we're talking about a system with a ruler flat frequency response and linear phase, we can be pretty sure it's linear.  In fact it's pretty tough to think of any non-linear system with a flat frequency response.  So I think if the FR is flat (meaning also that phase is linear), there won't be any distortion.

[Daryl]

No, because that assumes that the system is linear, which (since we are talking about distortion) it isn't.

Before Daryl gets all excited about this statement  don't forget that there are actually two things being discussed here: the time/frequency domain representations of a signal and the time/frequency domain response of a system.

Yes when speaking of a transfer function you have not only linear characteristics but also non-linear characteristics and noise characteristics.

If a componet is non-linear to much of a degree then it's linear transfer function will be unstable and trying to specify it's linear transfer function will become more and more useless as it's non linearity increases.

In Audio we have use only for systems which are very nearly linear.

Distortion must be miniscule for any acceptable componet and thus it's linear transfer function will be stable.

[Daryl]

Here is the situation(s) where the discussion of time/frequency domain does not apply.

Things like slew rate and square wave response apply when gauging the ability of an amplifier to handle unintended high frequency energy which can cause the feed back loop to become unstable (someone designing an amplifier would be looking at these things).

When an amplifiers feedback loop becomes unstable it's distortion will be gross and linear transfer function will be illrelavent until it recovers.

An amplifiers feedback loop should always be stable during normal operation.

There have been cases where manufacturers have built DAC's without lowpass filters at their output which send an excessive level of digital noise to the amplifier causing some of the more sensitive ones to become unstable.

Quality componets should be designed with reasonable levels of output noise and sensitivity to that noise so that any amplifier will be stable with any source componet.

On the other end of the amplifier the load can also cause it to become unstable.

An amplifier must be designed to handle a considerable range of load impedances and phase angles.

Load impedance will be important beyond the audio range for an amplifier all the way to the point where the magnitude of the feedback loops gain is less than one because the load impedance can influence the phase of the feedback turning negative feedback into positive feedback and causing the amplifier to become unstable.



 

[JohnR]

No, because that assumes that the system is linear, which (since we are talking about distortion) it isn't.

I think if we're talking about a system with a ruler flat frequency response and linear phase, we can be pretty sure it's linear.  In fact it's pretty tough to think of any non-linear system with a flat frequency response.  So I think if the FR is flat (meaning also that phase is linear), there won't be any distortion.

Hm... I'm having difficulty with this, since all amplifiers do have distortion... But suppose I had an amplifier that generated 10% second-harmonic distortion at any input frequency (as well as exactly reproducing the input signal), what would its frequency response be?

[Daryl]

Hm... I'm having difficulty with this, since all amplifiers do have distortion... But suppose I had an amplifier that generated 10% second-harmonic distortion at any input frequency (as well as exactly reproducing the input signal), what would its frequency response be?

A system with that much distortion might very well have level dependant fluctuations in frequncy response.

For us to consider an amplifier for hi-fi it must be nearly linear, nearly noiseless and nearly flat in frequency response which will result in a very stable linear transfer function.

You will evaluate it's frequency response not it's step/impulse response because your ears don't work like an oscilloscope and the frequency response curve applies better to the perspectiver your ears would have.

You will also evaluate it's non-linear distortion levels.

You will measure it's residual noise level and it's noise level with signals applied.

You will want to gauge it's immunity to unwanted high frequency noise at the input to insure it will be stable.

Lastly you will want to look at the range of load impedances and angles it can tollerate while remaining stable.

Also nice to know are CMRR, DC offset and power line noise rejection.

[bpape]

OK.  Time out.  Can't have it both ways.

If an amp with that much distortion has level dependent FR differences, then an amp with proportionately less distortion will simply have proportionately less level dependent FR differences - not no differences.

Bryan

[opaqueice]

Hm... I'm having difficulty with this, since all amplifiers do have distortion... But suppose I had an amplifier that generated 10% second-harmonic distortion at any input frequency (as well as exactly reproducing the input signal), what would its frequency response be?

I guess there's a semantic/measurement technique issue which could be getting in the way here.  The Fourier transform of the output would pick up that 10%, and then you couldn't call that response flat.  But if you measure or define FR in a more limited way, like by playing pure tones at some fixed level and then measuring the output only at the fundamental, then in your example that FR would look flat, it's true.    But that's a really special kind of non-linearity, which you picked carefully in order to ask that question  .

Linear systems are really special, and have lots of characteristics (for example that the amplitude of the response is linear in the amplitude of the input) which are highly unlikely to remain after some non-linear effect becomes important.  If we also specifiy linear phase, that means we've really nailed down the behavior of the system pretty well.  So while for any given measurement or definition of FR you're probably going to be able to find an example where that specific measurement doesn't detect the non-linearity, it's probably not very realistic.   Obviously any real amp won't have exactly flat FR or exactly linear phase, but if the deviations from that are small, I think we can be pretty confident that the distortion in the time domain output will be small too. 

[Dan Banquer]

"Obviously any real amp won't have exactly flat FR or exactly linear phase, but if the deviations from that are small, I think we can be pretty confident that the distortion in the time domain output will be small too. "

If you guys are really looking for time domain issues, you're not going to find much in amplifiers. You will find plenty of these type of issues in loudspeakers.

[JohnR]

Hm... I'm having difficulty with this, since all amplifiers do have distortion... But suppose I had an amplifier that generated 10% second-harmonic distortion at any input frequency (as well as exactly reproducing the input signal), what would its frequency response be?

I guess there's a semantic/measurement technique issue which could be getting in the way here.  The Fourier transform of the output would pick up that 10%, and then you couldn't call that response flat.  But if you measure or define FR in a more limited way, like by playing pure tones at some fixed level and then measuring the output only at the fundamental, then in your example that FR would look flat, it's true.    But that's a really special kind of non-linearity, which you picked carefully in order to ask that question 

Look, it's nothing to do with semantics or measurement technique. You simply cannot (fully) characterize a non-linear system using linear systems theory.

Now, where were we. I forget

[Dan Banquer]

Hm... I'm having difficulty with this, since all amplifiers do have distortion... But suppose I had an amplifier that generated 10% second-harmonic distortion at any input frequency (as well as exactly reproducing the input signal), what would its frequency response be?

I guess there's a semantic/measurement technique issue which could be getting in the way here.  The Fourier transform of the output would pick up that 10%, and then you couldn't call that response flat.  But if you measure or define FR in a more limited way, like by playing pure tones at some fixed level and then measuring the output only at the fundamental, then in your example that FR would look flat, it's true.    But that's a really special kind of non-linearity, which you picked carefully in order to ask that question 

Look, it's nothing to do with semantics or measurement technique. You simply cannot (fully) characterize a non-linear system using linear systems theory.

Now, where were we. I forget

Are you implying that if a linear system has some amount of distortion that it cannot be characterized by linear measurement techniques? If so what do you think should replace it?
       d.b.

[JohnR]

Unh 

I said cannot fully characterize a non-linear system.

Pretty pathetic trolling effort there, Dan.

[Dan Banquer]

You have answered about half the question I just asked, For the so called non linear reponses in linear systems how would characterize them?
If your responses to intelligent questions are accusations of trolling then I will glad to keep asking the question until I get a rational response. I do consider "I don't know" a rational response.
         d.b.

[opaqueice]

Look, it's nothing to do with semantics or measurement technique. You simply cannot (fully) characterize a non-linear system using linear systems theory.

If the Fourier transform of the output of a system is identical (meaning both amplitude and phase) to the Fourier transform of the input to that system, then the time domain output is identical to the time domain input.  That's an indisputable mathematical fact - it follows from the uniqueness and invertibility of Fourier transforms.  It's true regardless of whether the system is linear or not (actually it implies that it's linear, but it didn't require that assumption).

The catch is that we can't check the FT of every possible input, so we need to make some assumption about the behavior of the system for inputs we didn't check explicitly, such as that it's linear.  My point earlier was that you have to come up with something pretty contrived to produce a system which has this property over some reasonable set of signals (like a sweep tone) but isn't linear.

[JohnR]

You have answered about half the question I just asked, For the so called non linear reponses in linear systems how would characterize them?
If your responses to intelligent questions are accusations of trolling then I will glad to keep asking the question until I get a rational response. I do consider "I don't know" a rational response.
         d.b.

 

What's the question then? How do you measure distortion, is that it?

[Dan Banquer]

"The catch is that we can't check the FT of every possible input, so we need to make some assumption about the behavior of the system for inputs we didn't check explicitly, such as that it's linear.  My point earlier was that you have to come up with something pretty contrived to produce a system which has this property over some reasonable set of signals (like a sweep tone) but isn't linear."

I couldn't have said it better; thank you.
         d.b.

[JohnR]

The catch is that we can't check the FT of every possible input, so we need to make some assumption about the behavior of the system for inputs we didn't check explicitly, such as that it's linear.  My point earlier was that you have to come up with something pretty contrived to produce a system which has this property over some reasonable set of signals (like a sweep tone) but isn't linear.

Um, it only takes one counter-example to prove a hypothesis false...

Linearity is a model, a theory. It represents a useful approximation of your system/device/whatever if the behavior you're interested in is... well, that exhibited by a linear system. Which, if we're talking about distortion, it isn't.

And no, that doesn't invalidate the time-frequency relationship of a signal.

[Dan Banquer]

The catch is that we can't check the FT of every possible input, so we need to make some assumption about the behavior of the system for inputs we didn't check explicitly, such as that it's linear.  My point earlier was that you have to come up with something pretty contrived to produce a system which has this property over some reasonable set of signals (like a sweep tone) but isn't linear.

Um, it only takes one counter-example to prove a hypothesis false...

Linearity is a model, a theory. It represents a useful approximation of your system/device/whatever if the behavior you're interested in is... well, that exhibited by a linear system. Which, if we're talking about distortion, it isn't.

And no, that doesn't invalidate the time-frequency relationship of a signal.

O.K., If you have a counter example fine; please elaborate. If you do not have a counter example that's O.K. too.
             d.b.

[Daryl]

At no point was anyone trying to suggest that a linear transfer function is indicitave of non-linear characteristics.

The original topic was Synergy.

All the discussion about Fourrier, Distortion and amplifier stability is important to the Synergy issue because of the audio CLICHES' being thrown around.

Understanding that there is no truth to them is paramount to being able to understand any audio issue including Synergy.

A lot of comments being thrown around about there being things that can't be measured and if something does not appear in books it must not exist.

There are dozens of different measurements that can be used to characterize a componet and when the meaning of these is not fully understood it gives people the impression that maybe there are new types of measurement yet to be discovered that show things that all of the current ones don't show.

The truth is that there will be new types of measurements but they will show the same thing the already existing types of measurement show.

Most of the current types of measurements show the same thing that many of the others show.

The reason for their existance and that new types of measurements are introduced is not that you can't see that error with another type of measurement that you might use but that you simply would like a specific type of measurement that gives the clearest most direct portrayal of a particular type of anomaly that that applies to a particular situation.

Understanding that frequency domain and time domain are the same thing is a paradigm shift in the view of the audio universe for most audiophiles if you can get them to the water for a drink.

It is very common to hear someone commenting yeah the frequency response is flat but what about the time domain, you need to look at it's square wave resonse to see how it handles transients.

They don't understand that if frequency response is flat there is no signifigant time domain issue.

The point is not that frequency response can tell you about distortion the point is that frequency response is the same thing as impulse response and distortion does not change that.

A system being non-linear does not have any bearing on the fact that freqeuncy domain response indicates time domain response.

The system being non-linear simply means you have non-linear effects to add to the linear effects and the more non-linear a system is the more unstable it's linear transfer function will be.

Slew rate and square wave response are not quantities you would use to determine the sound of an amplifier but in fact are something you would use to determine under what circumstances that amplifier might become unstable.

[bpape]

There are dozens of different measurements that can be used to characterize a componet and when the meaning of these is not fully understood it gives people the impression that maybe there are new types of measurement yet to be discovered that show things that all of the current ones don't show.

The truth is that there will be new types of measurements but they will show the same thing the already existing types of measurement show.

Translation - We already know everything - the earth is flat.

My point was not that there might be new types of measurements - but new things TO measure.  What if at some point we find something that dismisses the need to assume systems are linear (IMO a bad assumption since NO system is perfectly linear - much less when having to interact with other dynamic, non-linear systems)?  What if the proof turns out to be different than the assumption?  Yes, what we know and assume now gets us pretty close, but not exact - and there is no 'e' to define that error as there is in calculus.  Is it even a constant 'e'?

Bryan