Waveform contains the info but it's easier to imagine using a spectrum analyzer.
IOW you can change a waveform visibly on a scope and it could be a linear or nonlinear thing that happened.
Do a FFT on the waveform and you will see effects on frequency response (linear) and amount of distortion (nonlinear distortion) as new spectral components.
No-no-no, you are calling nonlinear effects linear..
Nonlinearities cause 2nd harmonics (and others..).
The thing that causes new harmonic or non-harmonic components is a nonlinear function.
Please check out this presentation on "the sound of distortion". When a transfer function is not linear (flat) the output contains new (not present in the source) spectral components. Check out the magic box circuit where the curve can be varied at will. Probably similar to guitar distortion boxes.
http://www.pmillett.com/file_downloads/ThesoundofDistortion.ppt
http://www.pmillett.com/file_downloads/ThesoundofDistortion.ppt
I am completely misunderstanding something.
Please explain post22 in simple language that I and Turk can understand.
Please explain post22 in simple language that I and Turk can understand.
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This discussion is so much an example of how much misconception there is on this topic.
Some of the confusion has been cleared up but maybe not all.
Linear distortion will not change its effect for any signal content or level.
Nonlinear distortion'e effect is different for every signal level and every signal content. For example, clipping: it has no effect until it happens then its effect is pronounced. And a single tone will have only harmonics, but two tones will generate sum and difference tones of the two signals - different effects for different signal content. Using a large number of tones and one gets back noise - sum and difference between every pair and then some.
Finally, the presence of nonlinearity in a device, such as a long list of nonlinearities in a compression driver does not mean that any or all of these are actually audible, and at what level. This later question is very difficult to answer, but what studies have been done indicate that NLD is not a major factor in a loudspeaker.
Now take crossover distortion. At max signal level this distortion is only a few tenths of a %, but it is highly audible - one of the most audible of all forms of nonlinearity. How can that be. Its because for a very low level signal this form of distortion has very high orders of harmonics which are not masked. The amplifier guy calls this his "first watt" principle and it is exactly correct.
One problem with low level distortions like this is that they can be masked in the background noise of a broadband measurement, like THD + Noise. They won't even show up. But I developed a trick that reduces the noise floor while maintaining the distortion products and low and behold there were vast difference in amplifiers to be found in this test. So there is an audible difference between amplifiers that measure the same (usually standard test methodology.)
Clearly this is a complex issue that can be very hard to wrap your head around. My main point here has been, and remains, is that in a loudspeaker NLD is not a significant factor when a few well know design factors are implemented. This idea that lower the THD or IMD or any other measure of distortion is always a good idea is simply incorrect. Once the level have been brought out of the stratosphere, they fall below audibility - to wit, THD levels of 10-20% were not deemed to be audible in our tests. Claiming that a level of .1% distortion in a loudspeaker is audible is simply not possible.
Some of the confusion has been cleared up but maybe not all.
Linear distortion will not change its effect for any signal content or level.
Nonlinear distortion'e effect is different for every signal level and every signal content. For example, clipping: it has no effect until it happens then its effect is pronounced. And a single tone will have only harmonics, but two tones will generate sum and difference tones of the two signals - different effects for different signal content. Using a large number of tones and one gets back noise - sum and difference between every pair and then some.
Finally, the presence of nonlinearity in a device, such as a long list of nonlinearities in a compression driver does not mean that any or all of these are actually audible, and at what level. This later question is very difficult to answer, but what studies have been done indicate that NLD is not a major factor in a loudspeaker.
Now take crossover distortion. At max signal level this distortion is only a few tenths of a %, but it is highly audible - one of the most audible of all forms of nonlinearity. How can that be. Its because for a very low level signal this form of distortion has very high orders of harmonics which are not masked. The amplifier guy calls this his "first watt" principle and it is exactly correct.
One problem with low level distortions like this is that they can be masked in the background noise of a broadband measurement, like THD + Noise. They won't even show up. But I developed a trick that reduces the noise floor while maintaining the distortion products and low and behold there were vast difference in amplifiers to be found in this test. So there is an audible difference between amplifiers that measure the same (usually standard test methodology.)
Clearly this is a complex issue that can be very hard to wrap your head around. My main point here has been, and remains, is that in a loudspeaker NLD is not a significant factor when a few well know design factors are implemented. This idea that lower the THD or IMD or any other measure of distortion is always a good idea is simply incorrect. Once the level have been brought out of the stratosphere, they fall below audibility - to wit, THD levels of 10-20% were not deemed to be audible in our tests. Claiming that a level of .1% distortion in a loudspeaker is audible is simply not possible.
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Two other points:
A "transfer function" implies a linear system and as such there is no such thing as a nonlinear transfer function. the nonlinearity is usually described by the term "nonlinear transfer characteristic". I was corrected in this terminology when I first gave my paper by the great Stanley Lipshitz. He was correct and we should stick to this definition.
How fast or slow a nonlinearity progresses does not make a system linear. It is nonlinear if at any time in its limits of transfer - such as voltage, current, SPL etc. it exhibits a nonlinear characteristic. Thus all amplifiers would be non linear, because they will all clip at some point, (and if they are "gain limited" then this act in itself is nonlinear.) But below some definable limit they can be said to be linear (as long as there is no crossover distortion etc.)
The same thing is true for a loudspeaker, that at some point all loudspeakers can be played into their audibly nonlinear regime. In almost all cases of audible loudspeaker nonlinearity that I have seen it is pushing the driver beyond its design limits that is the culprit. There are always design limits, but they are seldom correctly defined in marketing specs.
A "transfer function" implies a linear system and as such there is no such thing as a nonlinear transfer function. the nonlinearity is usually described by the term "nonlinear transfer characteristic". I was corrected in this terminology when I first gave my paper by the great Stanley Lipshitz. He was correct and we should stick to this definition.
How fast or slow a nonlinearity progresses does not make a system linear. It is nonlinear if at any time in its limits of transfer - such as voltage, current, SPL etc. it exhibits a nonlinear characteristic. Thus all amplifiers would be non linear, because they will all clip at some point, (and if they are "gain limited" then this act in itself is nonlinear.) But below some definable limit they can be said to be linear (as long as there is no crossover distortion etc.)
The same thing is true for a loudspeaker, that at some point all loudspeakers can be played into their audibly nonlinear regime. In almost all cases of audible loudspeaker nonlinearity that I have seen it is pushing the driver beyond its design limits that is the culprit. There are always design limits, but they are seldom correctly defined in marketing specs.
are you and Lipshitz saying that a non linear transfer characteristic can exist? And does it follow that any signal distortion resulting from that is linear?
y = kx + q is a linear transfer function (multiplication by a constant and addition)
y = ax*2 + bx + c is non-linear and higher order functions are non-linear as well
(not considering frequency yet, just a static transfer function)
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There's no clipping until we reach the clipping level, so it makes no sense to speak about clipping below the clipping threshold 😀
No, not at all. The nonlinear transfer characteristic can exist and it will create a nonlinear distortion to any signal that is transferred through it. A "resulting signal" is neither linear or nonlinear, it is just a signal. The terms liner and nonlinear can only be applied to a transfer of signals, a process, not the signals themselves.
Just being pedantic, probably, but "Claiming that a level of .1% distortion in a loudspeaker is audible is simply not possible." Should that specify for only a non-broken loudspeaker? I can imagine a rubbing voice coil wire having crossover-notch-like distortion (maybe rubs only at one spot in the gap as the wire goes past?) being audible at very low percentage.
In my work, I defined the transfer characteristic as a polynomial, a Taylor series, in x where x is defined on some range < 1.0, as the signal levels normalized by the Max_Level. It become essential to define this Max_Level because without this definition nonlinearity cannot be uniquely defined. For example, if Max_level is defined to be below the amplifiers clipping range, then the amp is linear. If it is defined above it then the amp is nonlinear. This Max_Level thus become critical to define for any real discussion of nonlinearity.
As another example, in our tests Max_Level was, by necessity, lower than Max_Level in the other test of audibility of distortion in CDs. This makes it hard to compare the two tests, other than to say that at low levels of the other test they should agree with ours. I believe that they do. Hence, there is a level below which NLD is not audible and there is a level above which it is. Nothing surprising there I would have to say.
In a linear system, the transfer characteristic can only have the first term and second term:
y = a0 + a1*x
a0 would be the DC offset and a1 would be the gain. A nonlinear system might be
y = a0 + a1*x + a2*x^2 + a3*x^3 + ... an*x^n for an nth order nonlinearity.
I agree. Unless we know the distortion spectrum it is difficult to speak about thresholds of audibility. Also the already mentioned subharmonic distortion, low level is very audible. And, IME, it is not a general rule that speakers have just low order distortion components. Components of 9th order and higher are measured quite frequently.
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It can be shown that the order of the harmonic of a tone is exactly the same as the order of the nonlinearity. An nth order nonlinearity cannot generate harmonic orders above nth. This ties the distortion products directly to the nonlinear transfer characteristic.
Odd orders create only odd harmonics and vice-versa. Each order n creates an nth harmonic and modifies each alternate order beneath it. or example a 4th order will create a 4th harmonic and modifiy the 2nd harmonic and the DC offset. If there were no DC offset in the transfer then a DC offset would occur in the output.
The ear become more sensitive to the orders the higher they are. A loudspeaker will have very high 2nd and 3rd orders but they will (should) drop very fast after that. crossover distortion and clipping have many many orders, often above 10 and higher. This is why they are so audible. It is the order that matters, not the total level of the harmonics. Any metric that does not take this characteristic into account is going to be wrong. Its just the way that we hear and its not linear.
It can be shown that the order of the harmonic of a tone is exactly the same as the order of the nonlinearity. An nth order nonlinearity cannot generate harmonic orders above nth. This ties the distortion products directly to the nonlinear transfer characteristic.
Odd orders create only odd harmonics and vice-versa. Each order n creates an nth harmonic and modifies each alternate order beneath it. or example a 4th order will create a 4th harmonic and modifiy the 2nd harmonic and the DC offset. If there were no DC offset in the transfer then a DC offset would occur in the output.
The ear become more sensitive to the orders the higher they are. A loudspeaker will have very high 2nd and 3rd orders but they will (should) drop very fast after that. crossover distortion and clipping have many many orders, often above 10 and higher. This is why they are so audible. It is the order that matters, not the total level of the harmonics. Any metric that does not take this characteristic into account is going to be wrong. Its just the way that we hear and its not linear.
Bill, again, I could create a speaker that had horrible distortion at just a few %, but that's not the point. We are trying to create a system that is inaudible, not the other way around. but it is hard in these discussions to write down every assumption and caveat for every single statement, so things can get confused. thanks for pointing out that limitation to my claim.
Finally - I am assuming here that I want to make a speaker that is not broken, one with inaudible distortion.
All nonlinear systems are nonlinear, yes, but not all distortions are nonlinear, some are linear. A "distortion" is a result, not a system characteristic. Linear and nonlinear are characteristics of the system.
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