But the overall problem remains I'm trying to take a continuous waveform, discretize it, and then take that discretized waveform and make something continuous out of it again.
What do you mean the overall problem of “
trying to take a continuous waveform and discretise it …”
remains? It maybe remains in false audiophile marketing but it certainly does not remain in the real world. That “
problem” was actually solved in 1948 (by Claude Shannon), about 35 years before digital audio was even released to consumers!
So in the end all we have are these points in time, but no information about the smooth curve on which they connect to one another which will always impart a change to the sound.
NO! Again, you’re regurgitating false audiophile marketing as fact. Shannon proved in 1948 that 100% of “
information about the smooth curve on which they connect to one another” can be captured and therefore your assertion is false, it will NOT impart a change to the sound!
So the DAC designer has to figureout how to approch this problem and that decision will make an effect on the final sound.
Why would a DAC designer have to “
figure out how to approach to this problem” that was already figured out and proven 75 years ago? Are you referring to an 8 year old DAC designer in their bedroom who doesn’t know what digital audio is? This is typical audiophile marketing BS, state a problem that doesn’t exist or was solved decades ago and then sell a fake/snake oil solution to it!
As for approximations themselves how close of an approximation to a continuations waveform do you need to get before it no longer effects the sound perceptually, I don't know, but is of interest to me.
There is no approximation, the result (analogue signal) is ideal but with some dither noise. How that “
affects the sound” is easy to know/calculate, providing you know the basics of what sound is, and it’s physical limits. “Sound” can only exist within a range, it’s maximum is about 191dB SPL (due to the wave rarefaction pressure) and it’s minimum is about -23dB SPL (due to Brownian motion of air molecules). So, if you have dither (or jitter or any other noise) at say -120 dB and your peak listening level is at say 85dB SPL then that noise would be at -35dB SPL but as -35dB SPL cannot exist, it therefore CANNOT “e
ffects the sound”, even if you had hypothetically perfect speakers/HPs! However, anything, including absolutely no difference or effect on the sound whatsoever can affect perception, for example, false marketing.
And this is just the issues a perfect DAC might have, which can produce a specific voltage at a specific point in time -
Again, NO! That is an issue which a NOS/filterless DAC might have but that is the exact opposite of a “
perfect DAC”, it’s the most imperfect DAC topology anyone has has ever come up with, so much so that it’s effectively faulty/broken!
there is of course a host of electrical challenges then to the degree of accuracy you can accurately reproduce the individuated samples.
That doesn’t make any sense because (except with a filterless NOS DAC) no one is trying to “
reproduce the individual samples”, what is being reproduced in the electrical domain is a continuous (analogue) waveform. At that point, then yes there are a host of electrical problems, including the insoluble one of Johnson/Nyquist (thermal) noise, however we still have to compare that with the ultimate limit of sound itself and of course consider the problem further downstream of converting (transducing) that electrical analogue signal into a mechanical sound wave.
So tl;dr and to get back to the og question every DAC could be said to effect the sound in some way, you can scientifically measure what it is that the DAC is doing to that sound, but imo what exactly makes "good sound" or in this context "a good approximation" is not totally understood.
Again, that’s a falsehood, it has been “
totally understood” for more than 75 years and if it wasn’t, the digital age would not exist! The other problem is that contrary to another false assertion, you CANNOT “
scientifically measure what it is that the DAC is doing to that sound” or rather it might be possible but it would be extremely difficult and no one to my knowledge does. You can certainly measure what a DAC is doing to the analogue output and of course many do, but you cannot measure what it is doing to the sound because that analogue signal has to be amplified and transduced in order to become sound and that process adds far more distortion/noise than the DAC process. So how could we measure the sound and determine what distortion/noise the DAC process is causing rather than the amps, speakers and microphone, even if it would be enough to exist as sound in the first place?
In any case the point of the image and my statement on not having any information is to illustrate how (given an implied non infinite sample rate) given two sample points you will be making an approximation of the original waveform which will always lead to an inherent non neutrality of the DAC.
Just repeating the same falsehood assertions (false marketing) will not eventually somehow make them true! My explanation above, which you can fact check (
A Mathematical Theory of Communication - Claude Shannon - 1948) or on
Wikipedia, explains why it false.
You really should be sure of the facts before posting them in this forum, posting marketing BS/audiophile myths as fact is of course rather rude in a science discussion forum. If you’re not sure if you understand the audiophile claims or the actual facts/science, then please phrase your points as questions rather than assertions of fact!
G