syn08, I'm done here. I'm not sure if you simply don't know what you are talking about, or if you are gaslighting me. Your responses are becoming surreal.
At this point, I give you more credibility if I continue to argue with you.
At this point, I give you more credibility if I continue to argue with you.
Suppose an instrument like a guitar produces sound that is a function of multiple input variables: Pluck, temperature, humidity, etc. If we account for all of them (or enough of them to meet the required accuracy), so that we can predict the sound each time the instrument is plucked, is the appropriate model to use for the system time-invariant, or time-variant?
EDIT: I with Russel on his last post. I only wish the rude behavior had been dealt with more effectively over the years by those that can have some affect on it.
EDIT: I with Russel on his last post. I only wish the rude behavior had been dealt with more effectively over the years by those that can have some affect on it.
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I don't know how good the wikipedia page is Time-variant system - Wikipedia. but "Time variant systems respond differently to the same input at different times" seems to imply instruments are not time variant. However they are non-linear systems. Is it that the definition of time variance can be ambiguous?
You are talking about "system identification", which is, in itself, a big chapter in Control Theory. That is, find the differential equation (in general non linear and time dependent) of a system from it's response, when excited by a known input (say, a Dirac delta, or a Heaviside step). While this is rather simple for the case of linear systems, in the general case, this is a mission impossible and approximations as described above are required. That's all I can tell, the devil is in the details of the system to be analyzed, the magnitude of the non linear and time variant parts contributions, etc...
But enough "gaslighting"
, we are so far away from the original topic it is not even funny anymore... We started from the fact that non linearities in an audio amplifier create only harmonic distortions, and that time variant effects (like thermal distortions) need to be pathological for having an audible effect in an audio power amplifier.Hi, Scott.
From the link I posted a couple of pages back, from an electrical engineering course at UC-Berkeley: Time Invariance
You are correct that musical instruments are correctly thought of as time-invariant. The definition of time-invariance is not ambiguous. If I play a note in just the same way, now or in a few minutes, a properly functioning instrument will respond with the same note with the same volume and spectral properties.
From the link I posted a couple of pages back, from an electrical engineering course at UC-Berkeley: Time Invariance
In other words, if for all t ∈ Time, y(t) = (H(x))(t), then it must also be true that
y(t − τ ) = (H(x))(t− τ ).
A time-invariant system is one whose behavior (its response to inputs) does not change with time.
y(t − τ ) = (H(x))(t− τ ).
A time-invariant system is one whose behavior (its response to inputs) does not change with time.
You are correct that musical instruments are correctly thought of as time-invariant. The definition of time-invariance is not ambiguous. If I play a note in just the same way, now or in a few minutes, a properly functioning instrument will respond with the same note with the same volume and spectral properties.
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The definition is correct.
Pluck the string, you get say a 500Hz fundamental and it's harmonics. In each 2mS period, the properties of the instrument are changing due to the non linear string fixtures properties changes, as a function of the string oscillation amplitude. This leads to inharmonic components generation, kind of a "frequency modulation" (poor comparison, though, FM generates harmonic components relative to the carrier and modulation tone).
Finally, think of speakers; they are also mechanical time variant system, probably that's why some are considering speakers as "instruments 😀.
Yes, praying may help. But reading the relevant literature would be so much more helpful.
Authoritative reference to start with: KLIPPEL CONTROLLED SOUND see the patents.
P.S. Forgot to mention this one: https://www.fulcrum-acoustic.com/wp...dspeaker-transient-response-with-dsp-2005.pdf
Authoritative reference to start with: KLIPPEL CONTROLLED SOUND see the patents.
P.S. Forgot to mention this one: https://www.fulcrum-acoustic.com/wp...dspeaker-transient-response-with-dsp-2005.pdf
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Actually everything in the world is a time-variant, just we simplify some to time-invariant, otherwise we will never design some of it, like audio amplifiers.
In some physics theories time does not exist.🙁
In some physics theories time does not exist.🙁
The definition is what it says. IMHO what can be ambiguous is when we model a physical system mathematically, what is the best mathematical model for the purpose?
Hopefully, its becoming more obvious to more people that a physical system and a mathematical model of it are two different things. Engineers sometimes tend to lapse into language as though the model and the physical system are one and the same. Sometimes they even start believing it. IMHO, its healthy to remember that mathematics is a human invention. The physical world is as we find it.
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Thanks, makes sense, it's just a matter of degrees. I find my ear/brain combo to be the most time variant part of my system by far 🙂
And the threshold to hear distortion is?? Is there consensus about this question at least? This ego fight threads are not productive, let's make some sense of it...
Careful, Scott. Nothing that he said there is correct. He is describing a non-linearity mechanism, not a time variance mechanism. Nothing in the definition of time-invariance restricts how the system must respond to an input, so long as the system responds identically to identical inputs, regardless of when that input is applied.
Decay and non-harmonic modulation are valid responses, so long as it's the same decay and modulation every time.
But doesn't the non-linearity cause the time variance, however small? i.e. everything is time variant it's just that sometimes we can ignore it.
I could never understand why time variance is considered only regarding very long period changes, like thermal distortions. There's nothing in the definition of time variance that enforces such.
I've said already in this thread, if string instruments would not be time variant, then they would all, to a (harmonic) degree, sound the same. The sound (fundamental plus harmonics) would only depend on the material and the mechanical properties of the strings, plus the plucking technique (rendering the attack, etc...).
There is no consensus about threshold of distortion audibility.
I think less distortion is better, but we do not even have consensus about that. There does seem to be consensus that low order harmonics are better than high order, with good reasoning and psycho-acoustic testing to back it up. What the exact numbers are is not something we can get a definitive answer for. It does seem that some people are far more sensitive than others to distortion.
I think less distortion is better, but we do not even have consensus about that. There does seem to be consensus that low order harmonics are better than high order, with good reasoning and psycho-acoustic testing to back it up. What the exact numbers are is not something we can get a definitive answer for. It does seem that some people are far more sensitive than others to distortion.