[Roly1650]

Sure, that is what audiophilia is all about.  As a veteran of hundreds of bias controlled listening tests I can tell you that it is a fussy and boring business.  But comparing HD tracks to the same tracks downsampled to red book is an exception.  It is really easy to do and requires buying nothing.  It is more than religion.  It is stubbornness.

I bought into the hd tracks thing more than a few years ago and bought out soon after. Anything I ever downloaded didn't need downsampling, they were the same files just upsampled, even their "sampler" albums, which they claim are 24/96 are nothing of the sort. Upsampled 16/44, which is easy to see in Audacity. The standard patter is that they don't control the files, the original record label does, they only publish what they are given. But they also claim to carry out rigorous testing to ensure the files are what they purport to be. "Yea, right" is my answer to that.
Mind you, I should have known better, one of the artists they claim to have 24/96 files for has never let the original master tapes out of his possession and dumb me knew that at the time, live and learn.

 

[reginalb]

   
They still make no sense to me, since it's easy to fool yourself into believing sample 1 was better than the other at one time, then sample 2 was the one that was better the next time. If you get what I mean. The important thing is the resolution of the music. More bits/higher sampling frequency leads to capturing more of the original waveform. Anyone should be able to understand that. Bye.

 
Double blind ABX testing isn't about telling which is "better" but if you can distinguish a difference at all.
 
Sampling rate is the discussion at hand, the original waveform can be perfectly reproduced by a sampling frequency double the max frequency in the signal. This has been mathematically proven. For your assertion to be correct, you will have to prove one of two things (since you brought up that any idiot with a working pair of ears can hear a difference):
 

• You can hear signals above 22khz*
• disprove the mathematical proof. 

 
*And that some instrument produces sound at those frequencies. 
 
So you'll have to disprove a whole lot. But then again, maybe you're a dolphin, and you need to capture an ultrasonic recording that us humans can't hear. 
 
The OP from a couple years ago, was pointing out that some equipment can't even playback the higher sampling rate material properly, so if you hear a difference, it's distortion from the originally intended signal.

 

[castleofargh]

I just removed the bullying troll. this is the sound science section, please consider looking up the difference between Colbert's truthiness, and actual facts.

 

[gregorio]

I didn't see the post castleofargh removed but this part of the quote is interesting because it's so common on head-fi:
 
Quote:

  More bits/higher sampling frequency leads to capturing more of the original waveform. Anyone should be able to understand that.

 
I agree entirely, "anyone should be able to understand that". In fact, isn't that the whole point of a gross oversimplification in the first place, so that anyone can understand? The problem of course is that a gross oversimplification is not the actual facts, it's either extremely inaccurate, only true up to a point or both. The actual facts are a bit more complicated and "anyone" DOES NOT have the intelligence/ability to understand them.
 
MatsP, you repeating this gross oversimplification and stating anyone should be able to understand it tells us nothing except; about your personal ability to understand facts/your level of education!! If you actually do have the ability to understand but just lack the education, you can remedy the situation by answering this one question: With digital audio, why would (or wouldn't) we want to capture "more of the original waveform"?
 
G

 

[Baxide]

   
 If you actually do have the ability to understand but just lack the education, you can remedy the situation by answering this one question: With digital audio, why would (or wouldn't) we want to capture "more of the original waveform"?

I am not sure what education has got to do with it. Many discoveries and inventions were not the result of any particular education. 
As for the remainder of the sentence: it's easy to answer. We wouldn't because it would mean an immense of data that needs to be stored. At the same time, we would, because more data means better accuracy. What we have had to settle with is a compromise on a sliding scale and budget.

 

[gregorio]

  [1] I am not sure what education has got to do with it. [2] Many discoveries and inventions were not the result of any particular education. 
[3] As for the remainder of the sentence: it's easy to answer. [4] We wouldn't because it would mean an immense of data that needs to be stored. [5] At the same time, we would, because more data means better accuracy. [6] What we have had to settle with is a compromise on a sliding scale and budget.

 
1. Sorry to be blunt/harsh but that much is obvious, as every single one of the points you made is either partially or totally incorrect!
 
2. True, but not in the case of digital audio.
 
3. Not so "easy to answer" correctly though, apparently.
 
4. It wouldn't mean an "immense amount of data", it would mean an infinite amount. However, that's irrelevant because ...
 
5. Ah, the big and totally incorrect one! Beyond the optimum amount of data, we don't get more accuracy, we get less! The optimum amount of data was discovered by Harry Nyquist nearly 90 years ago and proven nearly 70 years ago. Two data points per audio frequency cycle allows for PERFECT reconstruction. You obviously can't get better than PERFECT reconstruction so more than two data points CANNOT give more accuracy, ultimately it can only result in less accuracy!
 
6. Partially true. Real world physical limitations of electronic components, engineering and budgetary constraints do cause compromises. However, these compromises have nothing to do with any lacking amount of data (as explained in #5) and today these compromises have been reduced to well below audibility, even with DAC chips costing just a few bucks!
 
G

 

[Baxide]

   
1. Sorry to be blunt/harsh but that much is obvious, as every single one of the points you made is either partially or totally incorrect!
 

You are not sorry. You are just being confrontational to everyone on Head-Fi because you like to be right even when you are dead wrong. Face up to that fact and start learning something from what others type, instead of dismissing everything that you did not come up with first. Some of us do have a university degree and even teach some of this stuff to students. We are not all uneducated you know.

 

[SoundAndMotion]

If you like to:
-complain about the level of intelligence/knowledge of people with whom you disagree
-"correct" their mistakes
you should be careful that the "correction" is itself correct!

4. It wouldn't mean an "immense amount of data", it would mean an infinite amount.

Well, I acknowledge that I'm picking nits here, but you created point #4. When you quoted MatsP saying "more of the original waveform" and Baxide said that would create an "immense" amount of data, let's be clear, capturing "more" means "more" data; capturing "immensely more" means an "immense" amount of data; but an "infinite amount" only happens if we try to capture ALL the data. Infinity is a really big number, you might remember.

5. (a) Ah, the big and totally incorrect one!
(b) Beyond the optimum amount of data, we don't get more accuracy, we get less!
(c) The optimum amount of data was discovered by Harry Nyquist nearly 90 years ago and proven nearly 70 years ago. Two data points per audio frequency cycle allows for PERFECT reconstruction.
(d) You obviously can't get better than PERFECT reconstruction so more than two data points CANNOT give more accuracy, ultimately it can only result in less accuracy!

(a) Well, it is perhaps "partially" incorrect, due to lack of specific conditions. More data does mean better better accuracy *IF* the signal doesn't have a limited bandwidth. Typically, either intentionally or just due to the physics of the system, a real signal has a limited bandwidth. Then there is a limit to the accuracy, as you try to point out.
(b) and (d) ??? I agree you can't do *better* than *perfect*, but how does having more data than necessary reduce accuracy? The extra data may be useless, but it doesn't reduce accuracy.
(c) I know what your mistake is, but since you like to task people try this: I have a 20kHz wave that you say is *perfectly* described with 2 points, or 40kHz sample rate. Now if the time, voltage (t, v) for those 2 points are (0µs, 0V) and (25µs, 0V), describe the wave. Interestingly, you can say something about the phase (which you like to ignore). It is n*180deg, where n is an integer. But you can say *anything*, let alone give a perfect answer, as to the amplitude.
Now if we have (0µs, +1V) and (25µs, -1V), you can't say anything about it. Is saying nothing perfect?

 

[castleofargh]

 

  [1] I am not sure what education has got to do with it. [2] Many discoveries and inventions were not the result of any particular education. 
[3] As for the remainder of the sentence: it's easy to answer. [4] We wouldn't because it would mean an immense of data that needs to be stored. [5] At the same time, we would, because more data means better accuracy. [6] What we have had to settle with is a compromise on a sliding scale and budget.

 
1. Sorry to be blunt/harsh but that much is obvious, as every single one of the points you made is either partially or totally incorrect!
 
2. True, but not in the case of digital audio.
 
3. Not so "easy to answer" correctly though, apparently.
 
4. It wouldn't mean an "immense amount of data", it would mean an infinite amount. However, that's irrelevant because ...
 
5. Ah, the big and totally incorrect one! Beyond the optimum amount of data, we don't get more accuracy, we get less! The optimum amount of data was discovered by Harry Nyquist nearly 90 years ago and proven nearly 70 years ago. Two data points per audio frequency cycle allows for PERFECT reconstruction. You obviously can't get better than PERFECT reconstruction so more than two data points CANNOT give more accuracy, ultimately it can only result in less accuracy!
 
6. Partially true. Real world physical limitations of electronic components, engineering and budgetary constraints do cause compromises. However, these compromises have nothing to do with any lacking amount of data (as explained in #5) and today these compromises have been reduced to well below audibility, even with DAC chips costing just a few bucks!
 
G

not sure what baxide said needed such answer.

it's wasn't even unreasonable.
 
the nyquist thing is true as long as we can do perfect band limiting. and we never do. I won't pretend it's always audible and important like so many do, but it keeps us from perfect reconstruction of everything. and some people will always want moar bits moar bandwidth, moar fries!!!! so it's only logical that manufacturers will do it if there is an obvious market. 
now you're perfectly right that too much is also a thing. if only because the devices we use don't have unlimited linearity at all frequencies, or unlimited speed.
 
anyway, we'll get what the manufacturers make, I doubt we will have much say in those decisions. the guy doing photocopies at apple probably has more weight on such decision than I do.

 
 
for the all education thing, I guess you understand how slippery it is on a forum. I'll just agree that one cannot really hope to understand digital audio with intuition alone. and hope we can leave it at that ^_^.

 

[gregorio]

not sure what baxide said needed such answer.

it's wasn't even unreasonable.

 
You're right, I was maybe overly harsh. I've had exchanges with Baxide before and allowed that experience to influence my response. For my part, I apologize to Baxide for the tone of my response.
 

Well, I acknowledge that I'm picking nits here, but you created point #4. When you quoted MatsP saying "more of the original waveform" and Baxide said that would create an "immense" amount of data, let's be clear, capturing "more" means "more" data; capturing "immensely more" means an "immense" amount of data; but an "infinite amount" only happens if we try to capture ALL the data. Infinity is a really big number, you might remember.

 
The point is, that with digital audio we don't need nor attempt to capture the original waveform. If that were the goal, we would need an infinite amount of data.
 

(a) Well, it is perhaps "partially" incorrect, due to lack of specific conditions. More data does mean better better accuracy *IF* the signal doesn't have a limited bandwidth. Typically, either intentionally or just due to the physics of the system, a real signal has a limited bandwidth. Then there is a limit to the accuracy, as you try to point out.
(b) and (d) ??? I agree you can't do *better* than *perfect*, but how does having more data than necessary reduce accuracy? The extra data may be useless, but it doesn't reduce accuracy.
(c) I know what your mistake is, but since you like to task people try this: I have a 20kHz wave that you say is *perfectly* described with 2 points, or 40kHz sample rate. Now if the time, voltage (t, v) for those 2 points are (0µs, 0V) and (25µs, 0V), describe the wave. Interestingly, you can say something about the phase (which you like to ignore). It is n*180deg, where n is an integer. But you can say *anything*, let alone give a perfect answer, as to the amplitude.
Now if we have (0µs, +1V) and (25µs, -1V), you can't say anything about it. Is saying nothing perfect?

 
A. Not sure I understand your use of the word "typically" here. In my experience as an audio professional, the signals are always band limited and of course, our hearing is also always band limited. So yes, provided you're talking about signals we don't record in the first place or can't hear anyway, my statement was incorrect.
 
B & D. That would depend on the amount/speed of the data. Try Dan Lavry's Paper on the issue.
 
C. No, I can't describe the 20kHz wave, And actually, I can't say anything at all about it's phase and all I can tell you about it's amplitude is that it effectively doesn't have any. I can't hear a 20kHz signal, so the only accurate description I personally can give is that it's either inaudible or doesn't exist. I'm willing to concede that under certain very rare/extreme circumstances some others might and therefore, to be on the safe side, I wouldn't recommend a 40kHz sampling frequency. By about 60kHz sample rate even all the theoretical issues disappear.
 
G

 

[Don Hills]

(c) I know what your mistake is, but since you like to task people try this: I have a 20kHz wave that you say is *perfectly* described with 2 points, or 40kHz sample rate. Now if the time, voltage (t, v) for those 2 points are (0µs, 0V) and (25µs, 0V), describe the wave. Interestingly, you can say something about the phase (which you like to ignore). It is n*180deg, where n is an integer. But you can say *anything*, let alone give a perfect answer, as to the amplitude.
Now if we have (0µs, +1V) and (25µs, -1V), you can't say anything about it. Is saying nothing perfect?

 
This is a common mistake. A 20 KHz signal can't be represented by a 40 KHz sample rate. The theorem only holds for frequencies LESS THAN twice the sampling rate.

 

[RRod]

   
This is a common mistake. A 20 KHz signal can't be represented by a 40 KHz sample rate. The theorem only holds for frequencies LESS THAN twice the sampling rate.

 
Assuming you want to represent all the way down to DC, that is.

 

[SoundAndMotion]

A. Not sure I understand your use of the word "typically" here. In my experience as an audio professional, the signals are always band limited and of course, our hearing is also always band limited. So yes, provided you're talking about signals we don't record in the first place or can't hear anyway, my statement was incorrect.

B & D. That would depend on the amount/speed of the data. Try Dan Lavry's Paper on the issue.

C. No, I can't describe the 20kHz wave, And actually, I can't say anything at all about it's phase and all I can tell you about it's amplitude is that it effectively doesn't have any. I can't hear a 20kHz signal, so the only accurate description I personally can give is that it's either inaudible or doesn't exist. I'm willing to concede that under certain very rare/extreme circumstances some others might and therefore, to be on the safe side, I wouldn't recommend a 40kHz sampling frequency. By about 60kHz sample rate even all the theoretical issues disappear.

A. When you brought up Nyquist, I put on my sampling/information theory hat and tried to make a true statement for the general case. You are of course right that we are in the head-fi/sound science forum and for all signals that we discuss here, they are all bandwidth limited. But Nyquist was not an audio engineer or neuroscientist, and the bandwidth (and therefore sampling rate) can be limited even more than the limits of audio (e.g. speech).

B and D. Again, in the sampling/information theory context, it does not depend on the amount/speed. But in the bandwidth limited case of audio and using current technology ADC’s, there is a speed/accuracy tradeoff. But for currently available ADC’s and DAC’s, does 192kHz reduce accuracy lower than 24 bits? If so, your point is good and current. If not, the amount/speed of data is not suffering from the speed/accuracy tradeoff. Great tip of the Lavry white paper, BTW, thanks.

C. I should not have used a 20kHz example, because of the question of audibility. You can hear 1kHz and it is not rare or extreme. But when your wrote ”Two data points per audio frequency cycle allows for PERFECT reconstruction”, that means a 2kHz sampling rate would be sufficient and it is not. By the way, you can say something about phase if you know the zero crossings, as I mentioned.

This is a common mistake. A 20 KHz signal can't be represented by a 40 KHz sample rate. The theorem only holds for frequencies LESS THAN twice half the sampling rate.

FTFY
Yes it is common to mistake the Nyquist frequency (fs/2) with the Nyquist sampling criterion (bw < fs/2), but when instructing others, as was done above, such mistake should be avoided.

Assuming you want to represent all the way down to DC, that is.

?? …which you would need to do to properly represent the signal, right? Even if we can only hear down to 20 Hz, a slow modulation of the envelope requires all frequencies from zero to the Nyquist sampling criterion. If I slowly turn the music up and down every minute, you need the lower frequencies, and you can hear that. I’m avoiding the philosophical discussion of whether we really need DC=0Hz, which has a period greater than the time since the big bang. I’m also avoiding the discussion of DC damaging speakers, by simply saying Fourier theory starts with DC and goes up the limit set by the criterion, and you may get a small non-zero DC value with a real-world signal.
EDIT: Fourier theory goes from DC to infinity. Nyquist-Shannon sets the practical upper limit required.

 

[RRod]

?? …which you would need to do to properly represent the signal, right? Even if we can only hear down to 20 Hz, a slow modulation of the envelope requires all frequencies from zero to the Nyquist sampling criterion. If I slowly turn the music up and down every minute, you need the lower frequencies, and you can hear that. I’m avoiding the philosophical discussion of whether we really need DC=0Hz, which has a period greater than the time since the big bang. I’m also avoiding the discussion of DC damaging speakers, by simply saying Fourier theory starts with DC and goes up the limit set by the criterion, and you may get a small non-zero DC value with a real-world signal.
EDIT: Fourier theory goes from DC to infinity. Nyquist-Shannon sets the practical upper limit required.

 
I'm just being overly pedantic. The theorem states you need twice the bandwidth, but doesn't require that this bandwidth start at 0. So if you were only interested in, say, 15-20kHz, you need a sampling frequency >10kHz, not 40kHz.
 
I'm not following you on the envelope. A frequency f amplitude-modulated at, say, 1Hz would show up on a Fourier analysis as f-1 and f+1, since there is the identity:
cos(x)cos(y) = 1/2(cos(x-y) + cos(x+y)),
which makes sense from the viewpoint of multiplication being dual to convolution.

 

[SoundAndMotion]

I'm just being overly pedantic.

Isn’t “overly pedantic” redundant? :rolleyes: (Now I’m being overly pedantic and probably wrong) As long as we’re both having fun and useful info is transferred, I don’t mind - I like it. “Learning is fun”, my mom used to say… when I try that on my son, he literally punches me.

The theorem states you need twice the bandwidth, but doesn't require that this bandwidth start at 0. So if you were only interested in, say, 15-20kHz, you need a sampling frequency >10kHz, not 40kHz.

I’d have to look up the exact wording/equations, but I’m certain that rather than bandwidth, one needs the highest frequency, i.e. always start from zero. Let’s consider your example moved down into the audible range, so no pedant comes back with “inaudible to old men”. Let’s say 1600-2000Hz, inclusive. So you claim that we would need >800Hz, for which 1000Hz works. Think it through: can I sample my 2000Hz pure tone at 1000Hz? No. I need >4000Hz. Is it clear? Perhaps you are thinking of amount of data. Yes, after I have sampled correctly and I do a Fourier transform, I can discard all the zeroes and make a much smaller file. True. But I have to sample at the higher rate first. I bet there is a way to create a special sampling process with a non-uniform sampling rate to have an average-lower sampling rate, but I assumed we are are talking uniform sampling rate.

I'm not following you on the envelope. A frequency f amplitude-modulated at, say, 1Hz would show up on a Fourier analysis as f-1 and f+1, since there is the identity:
cos(x)cos(y) = 1/2(cos(x-y) + cos(x+y)),
which makes sense from the viewpoint of multiplication being dual to convolution.

Yes, when I wrote “slowly turn it up and down”, beating, as in your equation, comes to mind. It would have been a better example to say “quickly”, such that the amplitude varies, not sinusoidally, but as a square wave. Turn it up for a second, then all the way down for a second, and repeat. You will have LOTS of very low frequency content. Even easier I think would be to just take some music you have and FT it. Don’t you see non-zero components all the way down to, but perhaps not including the first value (DC)?