yes you can reproduce a pure sine or sum of sinusoids as long as you're within nyquist and given there is no phase information that needs to be captured outside your sampling rate, you will have had in that case all the information between two discrete points such to reproduce a smooth curve between them.
Exactly, especially given that there is no phase information that needs to be captured outside your sampling rate!
You can think about it trivially by imagining some waveform and two samples on it, I could have a well defined curve between those two points or I could have a straight line, or for all I know or a 10000% spike in amplitude before returning back to the exact smooth amplitude I'd otherwise predict.
No, you can’t have a straight line and the amplitude is always smooth, even with a huge spike in amplitude!
Now for those things to happen I'd have to have some pretty high frequency components, which exceeded my sampling rate - but never the less they were there and you lacked the information to accurately reproduce that curve.
For the first thing to happen (a straight line) you would NOT need some “
pretty high frequency components”, you’d need to break the laws of physics and so obviously “
nevertheless they were there” is false! The second thing (a 10000% increase in amplitude) is well within the laws of physics, is not extremely uncommon and is well within the capability of 16/44.1, by nearly 3 orders of magnitude!
The other question to consider is what would happen if you did happen to sample or produce a sample on that amplitude spike and aliased down that higher order component.
What higher order component, why would you invent an ADC that aliased an amplitude spike and why consider a question that doesn’t exist?
In reality however the sound as it was emitted originally is unconstrained …
So you think that sound somehow magically avoids the laws of physics? The “
sound as it was emitted originally” was constrained by whatever emitted the sound (what freqs it actually produced in the first place) and by wave propagation in air (EG. Air absorption of high freqs as well as roughly the inverse square law). Then, when we capture the sound, we’re constrained by the mechanical limits of a microphone plus the limits of an amplified analogue signal.
yes you can filter it in such a way that you can offer some guarantee the x frequency components have been attenuated below audibility prior to sampling but now you've of course effected the signal.
What signal? The only signal we can digitise is an analogue signal, EG. A signal that has been captured by a microphone and amplified. And that signal is effectively identical up to the Nyquist point.
From what I've read there is still ongoing research into what the minimum phase and frequency discrepancies are detectable by the human ear.
No, there isn’t. What frequencies are detectable by the human ear was settled many decades ago and detectable differences in phase was settled several decades ago.
But as an engineer who professionally works on DACs for high speed control systems I've seen the inherent distortions a DAC (or more specifically any form of discretization) always imparts on a system, and given the jury is still out on what the ear can hear, it's my 2 cents as to where the non-neutrality problem originates from.
The human ear is not a high speed control system and the “
jury” is NOT “
still out on what the human ear can hear”, the jury returned the verdict in the 1930’s!
[1] I guess the question for you all then is, is the thought in general that any sample rate above 44Khz is pointless?
And [2) two, what then specific to the DAC itself colors sound? or is it thought to be a complete neutral component given typical CD quality sample and bit rates
1. It’s not pointless, there are various specific applications for sample rates above 44kHz. It is pointless for audio distribution however.
2. What “
specific to the DAC” audibly colours the sound is a faulty DAC design (such as a filterless NOS design) or a different output voltage but of course the latter can be neutralised by accurate volume matching. If a DAC is not audibly neutral (after volume matching), it is broken!
As BS by a scientist in a completely different field who doesn’t understand how audio works and is a disgrace! His papers (related to audio) are based on audiophile myths/misunderstandings, have been throughly debunked and discredited and he is treated as a joke (albeit a pernicious one). Many questioned the utter failure of the peer review process to weed out such BS papers before they reached publication, have heavily criticised the AES (and others) and demanded the papers be withdrawn. So severe was the criticism that the AES actually responded, along the lines (if I remember correctly) that their peer review process did not fail, they are well aware that the papers are incorrect but publishing them still serves the scientific and audio engineering community because they sparked so much debate. A BS response to cover their own asses, if they know the papers are wrong they should not have been published in a scientific journal in the first place and should have been withdrawn if published in error!
G
