Still not grasping this part of Sample Rates...

[Jac459]

Actually, I think you misunderstood because at some point I said oversampling when I was meaning upsampling.

My point is that upsampling from 44 to 88khz, doesn't give the quality of a native 88khz signal. Because half of its point would have been calculated and not measured. Period.
The quotation to know if the difference can be heard by non supermen people is secondary.

[avasopht]

My point is that upsampling from 44 to 88khz, doesn't give the quality of a native 88khz signal. Because half of its point would have been calculated and not measured. Period.

This isn't entirely correct (well ... let me backtrack a little and fill in the ... ... blanks).

You can upsample perfectly with a filter. I should have been clear that when I said upsample, I meant with a filter in place.

This is one of those numerical properties that are very well-proven in linear algebra.

This page explains it: https://www.wavewalkerdsp.com/2022/09/0 ... psampling/

It's a little counter-intuitive, but the waveform contains the complete frequency spectrum (and all points in between) ... with some fuzziness at frequencies close to Nyquist (and maybe 0 Hz). There are some YouTube videos that will explain it far better than I ever could. Forget about the points, and focus more on the linear algebra involved.

A PCM sample is an encoding of a continuous signal that just happens to look a lot like the PCM encoding is the wave itself.

It's not.

Suppose you record a 100 Hz sinewave. Instead of storing a PCM sample, you could just store that you played a 100 Hz sinewave, right? Alternatively, you could also just take a snapshot of the complete audio spectrum. Because the DFT transforms perfectly back and forth between the time and frequency domain we can say that the wave and frequency spectrum exist in a duality. The PCM waveform is also the frequency spectrum and vice-versa.

It just happens to be the case that a change in one domain has the same symmetric effect in the other.

And it turns out there's a limit to how much information is required to "discretely" represent a signal in either domain if we can assume there are no signals above a certain frequency. And this discrete representation will perfectly represent the entire signal and frequency spectrum.

Basically put, a PCM encoding contains all points in between. It's as good as saying, "a sine plays at 100 Hz and 224 Hz", except it can just tell you the wave amplitude or the frequency spectrum at any given point in time (up to Nyquist).

No additional information is required to perfectly reconstruct the signal. That is the Nyquist theory, and if you play around with the trigonometry and/or linear algebra, you could construct a proof of this.

Check out what zero-padding does with DFT (that's another method to interpolate).

And maybe ask on some DSP forums.

You can also intuitively reason about it by considering how your audio interface is somehow able to reproduce the exact signal from the 44.1 kHz PCM encoding (meaning it does in fact have enough information to perfectly reproduce it). If it did not, all audio interfaces would suffer from terrible and audible distortion.

[Jac459]

My point is that upsampling from 44 to 88khz, doesn't give the quality of a native 88khz signal. Because half of its point would have been calculated and not measured. Period.

This isn't entirely correct (well ... let me backtrack a little and fill in the ... ... blanks).

What do you mean by upsample perfectly ??


If you take Nyquist, 88khz will reproduce accurately 0 to 44khz range. So if you take your recording from 44khz, ranging 20 to 22khz and upsample it, will you start to have accurately the frequencies from 22khz to 44khz ? No you won't, you absolutely won't.
So it is mathematically incorrect.
I guess what you mean to say is perfectly... fine. 44khz to 88khz will be perfectly fine because nobody cares about ultrasound.

Is there any other points we disagree about ? I read your article as well as the remaining of your post but I feel we are saying the same thing...

[avasopht]

If you take Nyquist, 88khz will reproduce accurately 0 to 44khz range. So if you take your recording from 44khz, ranging 20 to 22khz and upsample it, will you start to have accurately the frequencies from 22khz to 44khz ? No you won't, you absolutely won't.

Agreed, if you upsample from 44.1 kHz (with filtering), you won't have any frequencies above 22.05 kHz. Without filtering you will get mirrored frequencies (for example if you just do it by zero-stuffing).

Note, that I was very clear that I was ONLY talking about reproducing frequencies below Nyquist (or the original sample rate, not the higher sample rate).

I guess what you mean to say is perfectly... fine. 44khz to 88khz will be perfectly fine because nobody cares about ultrasound.

Oh, I see the misunderstanding. It didn't seem that you were talking about frequencies that can't be produced at 44.1 kHz. Well of course, in that case, your ONLY option is to work at a higher sample rate.

But I recall you stating that rendering a sine wave at 44.1 kHz and upsampling to 88.2 kHz would not be as accurate as rendering the sine wave at 88.2 kHz because the 44.1 kHz wave would not have the in-between "points".

I understood that to mean you were talking about a sine wave that COULD be reproduced @ 44.1 kHz, not one that cannot (since attempting to render a frequency higher than Nyquist will just alias, with there being no in-between point).

But yes, you can't reproduce frequencies above Nyquist. I can understand the confusion now ... we were talking about completely different things

It's been a long day and I wasn't particularly well ... so I may have misread something ...

[Jac459]

If you take Nyquist, 88khz will reproduce accurately 0 to 44khz range. So if you take your recording from 44khz, ranging 20 to 22khz and upsample it, will you start to have accurately the frequencies from 22khz to 44khz ? No you won't, you absolutely won't.

Agreed, if you upsample from 44.1 kHz (with filtering), you won't have any frequencies above 22.05 kHz. Without filtering you will get mirrored frequencies (for example if you just do it by zero-stuffing).

Note, that I was very clear that I was ONLY talking about reproducing frequencies below Nyquist (or the original sample rate, not the higher sample rate).

I guess what you mean to say is perfectly... fine. 44khz to 88khz will be perfectly fine because nobody cares about ultrasound.

Oh, I see the misunderstanding. It didn't seem that you were talking about frequencies that can't be produced at 44.1 kHz. Well of course, in that case, your ONLY option is to work at a higher sample rate.

But I recall you stating that rendering a sine wave at 44.1 kHz and upsampling to 88.2 kHz would not be as accurate as rendering the sine wave at 88.2 kHz because the 44.1 kHz wave would not have the in-between "points".

I understood that to mean you were talking about a sine wave that COULD be reproduced @ 44.1 kHz, not one that cannot (since attempting to render a frequency higher than Nyquist will just alias, with there being no in-between point).

But yes, you can't reproduce frequencies above Nyquist. I can understand the confusion now ... we were talking about completely different things

It's been a long day and I wasn't particularly well ... so I may have misread something ...

Well I wasn't clear neither, saying oversampling for upsampling and overplaying the decrease of quality due to a conversion (for which I do agree with you both it is 100% negligible if even existant in the audible range), but now we understood eachother which is what matters hehe.

Actually, I must admit that my mind is a bit tricked because I am in a whatsapp group of hardcore audiophiles.
I am not myself an audiophile but they are interresting to discuss with.
This afternoon they were discussing about a LAN cable for audio that cost 900USD ...
One guy is saying that the quality of the electricity of his system is better in the morning.

So it is nice to have a discussion a bit more grounded in reality.

[RobC]

Alright, so then we can do all kinds of resampling, one better/worse than the other, and point is, the less often we do it, the better.

Again, great info to know!

That said, I still have no clue what the OP article meant by that above 60 kHz, the audio runs too fast. x D There could be two reasons: 1. That particular statement is BS (not Bachelors of Science : D) 2. They only consider recording and playback; but not really aliasing/anti-aliasing effects; and neither destructive sound design - and just want to discourage experimenting with higher sample rates for some reason.