He can not do with no abusive. Please ignore his abusive. Pretend you discuss with clever child. This is entertainment. 😀
Bimo is probably right, but I have to quibble with this statement more.
Except for tuning and aging, a musical instrument is a time-invariant system. A musical instrument being played by a musician is a time-variant system.
Unless that musician is a robot. But I digress.
Could you please quote at least an authoritative reference describing time variate/invariate systems, per your understanding?
Me abusive? I could say that abusive are those using smoke screens to defend their believes and knowledge (or lack, thereof).
For the rest, it is obvious you have no interest reading what I’m writing, so I’ll stop wasting my time. If you are interested in finding more about time variant/invariant systems, their properties and where the concept of “stationary” (which appears you are invoking) comes into, there’s a huge free library out there. I’ll leave you in Bimo’s companion, you guys are definitely resonating harmonically.
Last edited:
Why did you think anyone want your time? 😀
If you do not want to discuss, you are free to leave.
Russ, not sure if you are only trying to pull my leg here.
The reference you quoted talks precisely about time variant/invariant systems, their definition and high level properties. Exactly what I was trying to explain above. I must draw the conclusion that invariant==invariate and variant==variate in your own, private understanding.
???????????????
The reference you quoted talks precisely about time variant/invariant systems, their definition and high level properties. Exactly what I was trying to explain above. I must draw the conclusion that invariant==invariate and variant==variate in your own, private understanding.
???????????????
Perhaps you are not explaining it very well. Or perhaps you are missing the engineer's practical use of the time-invariant concept, which is to get to the end of the measurement with essentially the same system behavior with which you started.
Are you going to measure 1 kHz THD with a 10 second window to allow for heating? If you do, then you are probably correct to invalidate the assumption of time-invariance.
Or, rather, the system is still time invariant, but now we allow response to heating as another output variable.
Thanks. Then the notes are modulating each other via the mechanism of the piano?
What I'm not understanding is, if the piano is producing the intermodulation products that you mentioned earlier isn't that the result of intermodulation distortion caused by the mechanical system?
Yes, it would be. But what would be the cause of the piano doing that? The person playing it really hard/loud thus driving it a bit more into nonlinearity? If so, the question might arise, what should be considered to be 'the system' for our purposes? Just the piano, or the piano and player combined? Depends on the question or problem we are working on, wouldn't it?
Any string instrument is a time variant system. This happens because these strings have multiple vibration modes, one is the string "fundamental" with its harmonics (providing the "timbre") and one is the amplitude dependent vibration due to the nonlinear finite stiffness matrix of the wood at the string ends. One reason why aluminum neck guitars sound different from regular wood guitars.
Indeed the contribution of the player affects the magnitude of the time variant part, but it is the instrument that is fundamentally a time variant system.
But what has this anything to do with amplifiers and negative feedback? For all purposes, a well designed amplifier is a time invariant system; while thermal distortions are real and can be measured, if they are audible (which I am not convinced they are) then the amplifier is certainly of a pathological design.
P.S. This review addresses exactly these string instruments properties, I wish I had the time to go through in details. The practical interest in such studies (there are more) is related to electronically/DSP synthesizing string instruments.
Indeed the contribution of the player affects the magnitude of the time variant part, but it is the instrument that is fundamentally a time variant system.
But what has this anything to do with amplifiers and negative feedback? For all purposes, a well designed amplifier is a time invariant system; while thermal distortions are real and can be measured, if they are audible (which I am not convinced they are) then the amplifier is certainly of a pathological design.
P.S. This review addresses exactly these string instruments properties, I wish I had the time to go through in details. The practical interest in such studies (there are more) is related to electronically/DSP synthesizing string instruments.
Last edited:
A musical instrument is a time-invariant system. It doesn't matter if I pluck a string now or 5 minutes from now. If I pluck the string in just the same way, it will make the same sound. That is the very definition of time-invariance.
If instruments were time-variant being a musician would be much harder, and assembling a band or an orchestra would be impossible.
If instruments were time-variant being a musician would be much harder, and assembling a band or an orchestra would be impossible.
You obviously have a reading comprehension problem, mixed with a limited understanding of the time variant system definition; the string plucking period/frequency has no bearing here. Fact is, whenever a string is plucked, it vibrates in multiple modes, harmonic (based on the string properties and length) and inharmonic (due to the nonlinear finite rigidity of the string fixture). Therefore the output of the string pluck is a mixture of harmonic and inharmonic tones, which are characteristic of a time variant system. The only contribution of the player is the balance between the harmonic and inharmonic components, depending on the plucking way and amplitude.
If the link I provided is too hard to digest, then do yourself a favor and Google this; you'll find tons of material about this string instruments property. It appears to happen also in brass instruments. If string instruments would be time invariant, then they would all, in a first approximation, sound the same, based on the string properties and length.
If the link I provided is too hard to digest, then do yourself a favor and Google this; you'll find tons of material about this string instruments property. It appears to happen also in brass instruments. If string instruments would be time invariant, then they would all, in a first approximation, sound the same, based on the string properties and length.
Last edited:
So, if I have a dac that plays back a recording of a string being plucked, and I hide the dac inside a black box so nobody knows if it is a string being plucked or a dac is playing, then the black box contains a time variant system?
In general, no; you are trying to apply the superposition principle to a time variant system; that doesn't fly, and the answer is "we cannot decide". A correct approach would be to treat the system of string instrument + DAC as one system, estimate a "pluck" input (like a finite impulse, for example) and solve the nonlinear time dependent differential equations to get the response; which is obviously impossible in practice.
But perturbation theory comes to rescue, and tells that if the time variance is small, we can linearly separate the effects of the time variant and invariant subsystems, so accept the superposition principle for small variances. Then what you are saying is in principle correct, one could in principle not distinguish between the time variance of the string plucking and a possible time variance of the DAC response.
This is in theory, in practice we already know that a DAC has no reason to be considered a time variant system, at least not of the "magnitude" (poor defined here) of the plucked string instrument. It is the string instrument time variance that is the perturbation, not the other way around.
But perturbation theory comes to rescue, and tells that if the time variance is small, we can linearly separate the effects of the time variant and invariant subsystems, so accept the superposition principle for small variances. Then what you are saying is in principle correct, one could in principle not distinguish between the time variance of the string plucking and a possible time variance of the DAC response.
This is in theory, in practice we already know that a DAC has no reason to be considered a time variant system, at least not of the "magnitude" (poor defined here) of the plucked string instrument. It is the string instrument time variance that is the perturbation, not the other way around.
Last edited: