Why is distortion harmonic?

[Wavebourn]

It is absolutely a fact that no others exist. If they would exist, you would see them on the spectrum, simple as that.

When I record on CD a signal represented by an absolutely periodical function that decay exponentially and play it back I clearly see fuzzed lines and noises on spectrum, also I see how they change with level of a signal.

Would you be so kind to present a Fourier's row for such a transfer function?

THD was the first parameter that people started to measure using a sine wave of stable amplitude, but such a measure don't reveal all details, even when a stable sine wave that is periodical by nature is measured.

Edit: "If you wish to make an apple pie truly from scratch, you must first invent the universe." -- Carl Sagan

 

[ScottTracy]

When I record on CD a signal represented by an absolutely periodical function that decay exponentially and play it back I clearly see fuzzed lines and noises on spectrum

I'm afraid I'm having trouble visualising this. Could you make your description slightly clearer. Alternatively, providing a photo of the input signal and the output spectrum would be nice. Also, I think that you are coming close to looking like you are trying to start an argument about what measurements can or can't tell you which is completely off topic.


But basically, I think that the original question was answered beautifully by tubelab in post #5 and EC8010 in post #7. The question was why we get harmonics or multiples when we're measuring a non-sinusoidal waveform. Most of the answers have simply stated that that's what Fourier maths gives us. But to try to add to the good stuff said here already, if we put a pure SIN(wt) wave into an amp, this signal is going at a rate of w/2pi hertz. Since non-linear transfer functions simply act on this stimulus, the output should also be periodic with the same frequency. If you add multiples of the original signal to it in whatever proportions you like, the above condition will be met. If however, you add SIN(1.5*w*t) to it, the output will not have the same period. See fig.1. I guess you could call it a boundary condition in the time domain that when the input signal is at 0, the output should be too.

This of course only applies to simple harmonic distortion not motor-boating, blocking and so on which have already been mentioned.

Also, it may be worth pointing out that if you have a burst or pulse of some kind which only occurs once, it has components which are infinitely closely spaced in the frequency domain. It will have a continuous frequency spectrum rather than spikes or delta functions at integer multiples of some fundemantal. I would welcome any correction or further input on this one.

 

[AuroraB]

When I record on CD a signal represented by an absolutely periodical function that decay exponentially and play it back I clearly see fuzzed lines and noises on spectrum, also I see how they change with level of a signal.

If you see fuzzed lines and other components, and your input pulse is perfectly defined mathematically, the "extra" signals on your output is a result of exciting other processes than distorion . Your "extra" signals have no root in distortion theory whatsoever - and it's no use in questioning Fourier or the basis of general signal theory, as these are all the basis of all modern design and measurement methods. Also beware of your analysis tools, - they are all based on an adaption of the Fourier transform, and are not perfect.

If however, you add SIN(1.5*w*t) to it, the output will not have the same period. See fig.1. I guess you could call it a boundary condition in the time domain that when the input signal is at 0, the output should be too.

Not necessarily so, as there will always be time delays, furthermore, there might be linear distortion . Your picture is perfectly correct, but your 1.5wt is effectively a different frequency, that cannot be generated by distortion processes.

It may be that we should start asking questions of the measurement methods at hand, but I personally don't think so - it is more of developing an understanding of the interpretation of our modern measurements, like how do we interpret the distortion spectrum with respect to perceived sound quality.
In terms of theoretical processes, there is really nothing new under the sun - IMHO.

 

[Wavebourn]

You may think whatever you want, but the original question may be answered, "We measure harmonic distortions because we use such a method of evaluating electronics media". Period. Experience shows that such a method though common is not the best because less percentage of harmonic distortions may damage sound more than higher percentage of harmonic distortions.

We may measure for example angles of aberration of a transfer function's curve against a straight line, in such case the question would be, "Why all distortions are measured in angles?" Or, "Why all distortions are tangential"? Answers: "Because Wavebourn said so", or "All distortions are tangential".

 

[AuroraB]

JahhJahh....
Wavebourn has spoken...goodbye Fourier
sigh..........

 

[jan.didden]

You may think whatever you want, but the original question may be answered, "We measure harmonic distortions because we use such a method of evaluating electronics media". Period. [snip]

Wrong. You have it backwards. We measure harmonic distortion because the non-linearity of a device produces harmonic distortions. If the non-linearity of a device would produce doppler shift, we would be measuring doppler shift. Really simple, when you think about it.

Jan Didden

 

[Wavebourn]

Wrong. You have it backwards. We measure harmonic distortion because the non-linearity of a device produces harmonic distortions. If the non-linearity of a device would produce doppler shift, we would be measuring doppler shift. Really simple, when you think about it.

You look from the wrong prospective. Non-linearity may be measured by angles. Any non-linearity. Without any complex transformations. Because a curve is direct graphical representation of a function. In order to get harmonics you need to apply a sinusoidal signal then analyze it using Fourier transformations. Transfer function itself don't contain Fourier transformations. But it's graphical representation has a shape that may be measured by simple geometrical instruments.

"Means of Measurements" and "Essential Properties" are different things, right? Really simple, when you use Okkam's Razor.

 

[jan.didden]

You look from the wrong prospective. Non-linearity may be measured by angles. Any non-linearity. Without any complex transformations. [snip]

So, how would that work then?

Jan Didden

 

[Wavebourn]

So, how would that work then?

It will work by measurement of angles, like tangent of degree of losses works in RF design. The higher is SPL, the higher degrees are forgivable since our perceptions may be represented by logarithmic function. Take an exponential signal and measure deviations from it. Very simple. You may take a periodical one, from zero to +rail, from zero to -rail, and observe it on the oscilloscope (or calculate deviations using AD converters).

However, such a measure is very inconvenient for modern industry because mainstream differential inputs and complementary emitter followers for outputs would be considered as worst approaches for audio reproduction.

 

[jan.didden]

It will work by measurement of angles, like tangent of degree of losses works in RF design. The higher is SPL, the higher degrees are forgivable since our perceptions may be represented by logarithmic function. Take an exponential signal and measure deviations from it. Very simple. You may take a periodical one, from zero to +rail, from zero to -rail, and observe it on the oscilloscope (or calculate deviations using AD converters).

However, such a measure is very inconvenient for modern industry because mainstream differential inputs and complementary emitter followers for outputs would be considered as worst approaches for audio reproduction.

.. but how would it work? I mean what exactly do you measure? And how does that relate to the non-linearity of the device in question?

Jan Didden

 

[Wavebourn]

.. but how would it work? I mean what exactly do you measure? And how does that relate to the non-linearity of the device in question?

I generate an exponential function (currently I use analog generator, made of an oscillator, D-trigger, R from one output, C from other output), and 2-ray oscilloscope. I plan to use D/A converter to generate a function and 2 - channel A/D to compare and measure angles. It shows me aggregated "audible distortions" clearly, and such measurements correlate well with listening tests. What was "cutting edge" technology when electric machines were used to generate a sine wave is a stone age today.

I measure weighted against perceptions non-linearities instead of "an average temperature of patients in a clinic" like in case of THD measurements.

Edit: Surprise, using such measurements I've found A+C amplifiers more linear then AB amplifiers! That explained why listeners preferred them (like my Swinnik and Piranha designs)

 

[Wavebourn]

If my measurements take over the world expect a revolution: logarithmic A/D and D/A converters for audio instead of linear ones.

 

[jan.didden]

If my measurements take over the world expect a revolution: logarithmic A/D and D/A converters for audio instead of linear ones.

I can see that. I mean, apart from the fact that your last couple of posts are pupukaka to me, if its true you really are on the verge of taking over the measurement world. Must be a great feeling

Maybe a small tip: instead of talking in such a way as to hide what you really mean, people might be easier to convince if you try to be clear. I assume you DO know what you're talking about, of course.

Jan Didden

 

[AuroraB]

I really had decided to leave this thread for good, but I jusst can't keep myself

I measure weighted against perceptions non-linearities .

You mean you taylor your measurements towards what you want to see, rather than towards what might be the fact?

Edit: Surprise, using such measurements I've found A+C amplifiers more linear then AB amplifiers! That explained why listeners preferred them (like my Swinnik and Piranha designs

 

[Wavebourn]

Instead of taking over the measurement world I would be glad to make some money on selling audio devices developed using such measurements.

 

[Wavebourn]

You mean you taylor your measurements towards what you want to see, rather than towards what might be the fact?

A bit different: I want to see facts that people hear instead of fact that people don't hear. If you disagree why are you still in vacuum tube's forum instead of SS one? Their designs are better according to "standard" measurements than designs on this one.

 

[jan.didden]

A bit different: I want to see facts that people hear instead of fact that people don't hear. If you disagree why are you still in vacuum tube's forum instead of SS one? Their designs are better according to "standard" measurements than designs on this one.

"Facts that people hear" Haha! Are you sure you don't want to post this in the "more engineering humor" thread?

Jan Didden

 

[EC8010]

To get back (slightly) to the thread topic, you could measure distortion by plotting the transfer characteristic directly, or its differential. But in most cases, the distortion is sufficiently low that it's difficult to do, whereas applying a sine wave, filtering out the fundamental, then measuring the residual is easier.

The differential of a reasonable transfer characteristic should be a constant DC with deviations, so AC coupling it and amplifying would give just the deviations. I suspect that noise would be a problem...

The thing is, for all the criticisms levelled at it, measuring harmonic distortion is a good way of quantifying nonlinearities, and a harmonic weighting filter can always be added before the meter.

 

[Wavebourn]

"Facts that people hear" Haha! Are you sure you don't want to post this in the "more engineering humor" thread?

No, I am going to post end results to people who prefer to listen to the music instead of to listening to orthodox engineers who has neither physics nor psychology background.

 

[EC8010]

Attack ideas, not people.



This thread is leaning towards temporary closure territory. Don't make me do this...