I suspect he knows that perfectly well. There's language/translation issues here.
I was actually refuting what you wrote: "Only time-variant systems ... can create inharmonic artifacts..." I'm thinking this sentence doesn't mean what you intended it to mean. Time invariant systems can and do produce inharmonic artifacts. As can time-variant systems.
We were discussing (I think) thermal drift. The audibility of thermal drift won't show up as a THD directly, it will show up as a change in the harmonics of a system. Imagine the same piano, but heat it up (retuning as you go). It will sound different before and after heating, but the heating is too slow to have a directly audible artifiact.
The only exception I know of is IC power amps. When the LM12 came out, it's self-heating was fast enough that it made low frequency THD worse. The output transistors heated the input pairs quickly enough to cause distortion. Measurable and audible.
I was actually refuting what you wrote: "Only time-variant systems ... can create inharmonic artifacts..." I'm thinking this sentence doesn't mean what you intended it to mean. Time invariant systems can and do produce inharmonic artifacts. As can time-variant systems.
We were discussing (I think) thermal drift. The audibility of thermal drift won't show up as a THD directly, it will show up as a change in the harmonics of a system. Imagine the same piano, but heat it up (retuning as you go). It will sound different before and after heating, but the heating is too slow to have a directly audible artifiact.
The only exception I know of is IC power amps. When the LM12 came out, it's self-heating was fast enough that it made low frequency THD worse. The output transistors heated the input pairs quickly enough to cause distortion. Measurable and audible.
Yes. Mechanically and acoustically. Lots of crosstalk and feedback mechanisms, and non-linear responses. Resonances, too, that affect the magnitude of harmonics, but are not themselves generators of them.
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Example please? This would be a new one for me. I am talking about amplifiers, not musical instruments, which I am afraid ARE time variant systems.
No, IMD is not generally produced through acoustic means alone, except at very high dB-SPL, where air becomes non-linear. (You can't rarify air beyond 0 atm pressure, but you can pressurize it many atm pressure.)
No, it's the mechanical parts (wires, frame, and wood) that produce the harmonics. If they produce harmonics, they also produce IM products.
No, it's the mechanical parts (wires, frame, and wood) that produce the harmonics. If they produce harmonics, they also produce IM products.
DAC aliasing is like the beats produced in musical instruments. Beat frequencies are also an aliasing phenomenon, but linear.
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Beats physically seem to be a sort of interference pattern when mechanical vibration frequencies are added. Aliasing is different in that an FFT will show a new frequency has been created.
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I think I see the disconnect. You're saying time-invariate systems. But time-invariate systems often have time-variate signal inputs.
The difference between a system playing music and a system playing a periodic test signal.
Sorry if I'm conflating IMD and IM products. I do not mean to. It is probably wrong to think of musical instruments having distortion. It depends on what the reference is. Generally, the reference is the instrument itself. But it could be another instrument, or a pure tone. Of course, electric guitars have lots of distortion. Which you would want a sound reproduction system to reproduce exactly.
But yes, I mean IM products, not distortion. OTOH, if one piano plays purer notes, does the other one have distortion?
But yes, I mean IM products, not distortion. OTOH, if one piano plays purer notes, does the other one have distortion?
+1000
How can amplifier which amplify signal from musical instrument can have different system? I didn't get it.
Never heard of time invariate, only heard of time invariant and time variant systems. Obviously time invariant systems have time variant input signals, unless they are DC amplifiers where "distortions" make no sense.
There is no difference between a system playing music vs. playing a periodic test signal, except for the Fourier deniers team.
Because we are at it, the Fourier theorem makes no assumptions about the linearity of the system (or periodicity of the signals), the only condition is that the functions are "sufficiently continuous" (and I'll stop expanding on the math here).
Unfortunately for many, there is a big cloud of confusion between the "Fourier series/expansion" (the foundation for FFT) and the "Fourier transform" (the foundation for circuit analysis in the frequency domain). They overlap if and only if the system is time invariant and we enforce the signal periodicity condition. The response of a time variant system to a periodic signal does NOT necessary have a Fourier series/expansion (or a FFT, if you prefer a loose expression), unless the input signal and the system time variant parameter(s) are harmonic.
If there is "sufficiently continuous" then there is no thermal distortion because thermal does not change.
That explains why you don't get why others don't get what you are saying. Doesn't mean you have to be abusive. Time varying signals can be applied to time invariate systems.
Time variate doesn't mean DC, it just means not steady state, i.e, aperiodic.
The rest of your post actually supports what I am saying. Aperiodic signals can have energy content at different frequencies. Non-linearities, distortion, and modulation characterized in a time-invariate analysis will still occur. The phenomena are just harder to quantify outside of steady-state analysis.
Even an FFT, which imposes its own periodicity, is junk unless it is windowed carefully, or it's periodicity matches that of the steady-state signal being analyzed.
Yes, really.
If the thermal changes are slow compared to audio frequencies, then the thermal can be considered invariate for audio analysis. You may have to do the test twice, once cold and once hot, but neither test will directly show non-linearity due to a dynamic thermal mechanism. The result is only seen in the comparison.
Again, look the THD vs Frequency for an LM12. Thermal feedback to the input stage occurred with a small enough time constant that THD measured higher below 100 Hz. This does not happen with discrete amplifiers.