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Old 11th March 2008, 12:48 AM   #21
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Quote:
Originally posted by janneman



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

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Old 11th March 2008, 12:36 PM   #22
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Quote:
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.
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Old 11th March 2008, 02:05 PM   #23
AuroraB is offline AuroraB  Norway
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Quote:
Originally posted by Wavebourn


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.

Quote:
Originally posted by ScottTracy

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.
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Old 11th March 2008, 05:24 PM   #24
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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".

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Old 11th March 2008, 07:06 PM   #25
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Old 11th March 2008, 07:22 PM   #26
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Quote:
Originally posted by 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. [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.

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Old 11th March 2008, 08:12 PM   #27
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Quote:
Originally posted by janneman



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.
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Old 11th March 2008, 08:14 PM   #28
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Quote:
Originally posted by Wavebourn
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?

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Old 11th March 2008, 08:39 PM   #29
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Quote:
Originally posted by janneman



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.
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Old 11th March 2008, 09:10 PM   #30
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Quote:
Originally posted by Wavebourn


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?

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