Digital audio fundamental question

Okay, let's continue with the same experiment but in a different way.
Assumption no 1: You don't know the frequency.
Assumption no 2: You take 2 measurements of the displacement from neutral position, spaced 1 sec apart.

Now, take a pencil, draw the neutral position. Place these 2 measurements of displacement on the chart as X, time as Y. Draw a wave. Let's see if we can get an accurate one.
If the frequency is more than a second, it cannot be accurate.
 
Well well. You were saying a minute ago that the eardrum moves in a sine wave.. So not sure if you are saying the ear drum moves differently from a driver??

Perhaps I should apply for the no-bull prize instead because that is what I am trying to clarify to myself.

And perhaps you should back up your stand with more detail than the one liners you are providing. For example:
1. How do you think our brain and ear is able to understand a 20hz tone? I get that it waxes and wanes with the wave. But how does it differentiate between 20hz and 21hz?
2. Do you also believe that our ears capture sound in a continuous way? If so, how?

Yes, the ear drum moves back and forth as well. And you tell me if our brain can tell whether the sound is at 20 hz or 25 hz or 1000 hz.

And where did I say that ears capture it continuously? I said the creation and record events are discrete. But the sound wave is continuous. The sound once created moves in continuous fashion till it dies. I will tell you what, show me one article which says sound wave is not continuous after its created.

Another thing - each sound wave will have different amplitude at various distance. Good example of this is low frequencies because those waves are quite long. Place a subwoofer at the center of a wall. Play a 60 hz sine tone (for simplicity). Now you can use a measuring microphone or even SPL app in iphone. Start from the subwoofer while the tone is playing. Start walking towards the opposite wall. You would see the SPL changing. But you will not notice its on/off/on/off. Its a continuous wave.
Now, to come back to one note - yes, woofer playing is a discrete event. But once that done, the wave generated is continuous for that time, it will go to the backwall, reflect from it and start coming towards front wall. At that point if the signal is still playing, it will do cancellation with incoming signals. The whole acoustic solutions are to take care of reflections, standing waves and room modes for this reason. We wouldn't be talking about those.
 
If the frequency is more than a second, it cannot be accurate.

Yes, exactly. See, the Analog to digital conversion method does not know what frequency it is. All it has is amplitude data at a particular time intervals (for CD's, 1/44100 seconds to be precise) That's why it needs more data to predict the frequency and waveform. It can still predict a waveform, but it wont be close enough to original, causing aliasing.
 
Yes, exactly. See, the Analog to digital conversion method does not know what frequency it is. All it has is amplitude data at a particular time intervals (for CD's, 1/44100 seconds to be precise) That's why it needs more data to predict the frequency and waveform. It can still predict a waveform, but it wont be close enough to original, causing aliasing.
At 44100 times a second sampling rate, it has the complete information for all frequencies up to 20000 times a second, i.e., 20khz, with a margin of safety. No predictions needed. Because the number of times the sampling has been done is in excess of the time intervals involved in those frequencies.
If there are frequencies in the signal above the sampling frequency, that is when aliasing happens, which is addressed by an anti aliasing filter. This is done to eliminate the undesirable aliasing effect of inaudible frequencies on audible ones - assuming that even 20khz is audible to most adult humans!
 
At 44100 times a second sampling rate, it has the complete information for all frequencies up to 20000 times a second, i.e., 20khz, with a margin of safety. No predictions needed. Because the number of times the sampling has been done is in excess of the time intervals involved in those frequencies.
If there are frequencies in the signal above the sampling frequency, that is when aliasing happens, which is addressed by an anti aliasing filter. This is done to eliminate the undesirable aliasing effect of inaudible frequencies on audible ones - assuming that even 20khz is audible to most adult humans!

Yes, exactly. Hence the importance of double sampling rate.

Now, if a recording is with 96Khz sampling rate, then it does not mean it will have frequencies upto 48 khz. It can store that much comfortably. But the entire chain has to be upto 48 Khz, like instruments playing, recording mics, all the mixers etc should also be 48 Khz capable. But the benefit is that there is no steep rolloff after 22Khz like CD, but rather a gradual one. And there is more sampling data at 20 Khz. How much useful? Depends upon our hearing and capability of the playback system.

I think we have now come onto same page. :clapping:
 
Yes, exactly. Hence the importance of double sampling rate.

Now, if a recording is with 96Khz sampling rate, then it does not mean it will have frequencies upto 48 khz. It can store that much comfortably. But the entire chain has to be upto 48 Khz, like instruments playing, recording mics, all the mixers etc should also be 48 Khz capable. But the benefit is that there is no steep rolloff after 22Khz like CD, but rather a gradual one. And there is more sampling data at 20 Khz. How much useful? Depends upon our hearing and capability of the playback system.

I think we have now come onto same page. :clapping:
We are close enough, but save some clapping for a bit longer:).
You are now largely moving out of theory into practice.
But first, yes 96khz sampling rate will have frequencies up to 48khz. If there is any being produced with enough energy to be heard,even if human hearing were to reach those levels, which it doesn't.. And recorded of course, that is a valid point you have made too.
And for frequencies above 22khz, there is a steep rolloff on CD. No doubt. A but will follow later:).
By the way, how come you missed the 16 bit to 24 bit part of this saga?
Where I disagree with you in theory is this:
There is more sampling data at 20khz. But it doesn't add a jot of extra " value". If I already have a sample of all the necessary information why do I need more? There would be no use of that extra data up to 20khz for anyone, from bats to Superman to Mr Golden Ears Audiophile. It also doesn't add any value to the playback system.
There is one other thing to remember about 24/96. I don't know the theory, and I haven't the experience of this - I can only recount something I have read. With that upfront admission, it seems that 24/96 can, in some cases, actually introduce distortion of some kind in the frequencies upto 20Khz. In practice then, it can be a possible loss/no audible win situation.
Now, to the but I referred to earlier:
Other than the supposed distortion referred just above, all the theory about 24/96, even if 100% correct, means nothing - to me at any rate - if the difference between CD and Hi res cannot be distinguished in a level matched AB blind test.
The problem is that Hi res music is also often remastered with more care than the older CD, and usually this is done by the mastering studio A team. This remastering will sound audibly better, depending on how well it is done, and how lousy the original CD mastering was. To eliminate this variable, one needs to downsample the HD files to 16/44 or 16/48, and then still identify the differences in a rigourous listening test. If found, this is a validity of audible superiority of 24/96, mastering differences being eliminated. In the absence of audible benefits, this is poor engineering, being unnecessary use of resources.
Afaik, no one in the world has established such a difference in such a test.
By the way, you do know that people are talking about 24/384 now?
 
Yes, the ear drum moves back and forth as well. And you tell me if our brain can tell whether the sound is at 20 hz or 25 hz or 1000 hz.

And where did I say that ears capture it continuously? I said the creation and record events are discrete. But the sound wave is continuous. The sound once created moves in continuous fashion till it dies. I will tell you what, show me one article which says sound wave is not continuous after its created.

Another thing - each sound wave will have different amplitude at various distance. Good example of this is low frequencies because those waves are quite long. Place a subwoofer at the center of a wall. Play a 60 hz sine tone (for simplicity). Now you can use a measuring microphone or even SPL app in iphone. Start from the subwoofer while the tone is playing. Start walking towards the opposite wall. You would see the SPL changing. But you will not notice its on/off/on/off. Its a continuous wave.
Now, to come back to one note - yes, woofer playing is a discrete event. But once that done, the wave generated is continuous for that time, it will go to the backwall, reflect from it and start coming towards front wall. At that point if the signal is still playing, it will do cancellation with incoming signals. The whole acoustic solutions are to take care of reflections, standing waves and room modes for this reason. We wouldn't be talking about those.

So you say that creation of sound is discrete, recording is discrete, and the way our brain detects sound is also discrete. So my original question was - why do you care if the sound wave was analog/continuous or not?

The original question was whether digital recordings can perfectly store music within our hearing range or not.

We see this all the time. Audiophile equipment manufacturers get into deep level physics and when someone makes a practical argument about how these physics principles are relevant, the standard strategy is to go even deeper into physics. I guess the strategy banks on the fact that most audio enthusiasts are not usually double PhDs in physics so when faced with esoteric physics, they will never be able to prove or disprove anything.

I have only studied a bit of physics but at least enough to hold a hopefully decent conversation. If you really want to get into a theoretical physics argument about the true nature of waves and the true nature of matter, there are layers upon layers of logic. Like I mentioned earlier, if you want to properly argue this, you can get down all the way to quantum mechanics - where all your smooth looking waves become discrete entities again.

The thing to note is that all these are mathematical and theoretical models. Meaning - that perfect looking sine wave? It is neither perfect in real life nor does it even look like Michael Jackson doing break dance.

Ultimately what matters is how we interact with these physical phenomena, namely sound. So if my ear hairs get vibrated 20 times a second for me to hear a 20hz note, and if a digital recording claims that it stored at least 40 samples of the original vibration, and can thus re vibrate my ear hairs 20 times a second when I press the play button, it makes sense to me that the digital recording is telling the truth. Whether the theory of relativity was involved in the wave being transmitted is irrelevant, at least for me. I only care that my ear hairs be re vibrated with the same level of accuracy when I heard the instruments being played live.

I will not be able to have a discussion with you if you are taking this discussion to a topic that is about the purity of the wave or not. I do not have that level of knowledge, honestly speaking.

And I was also saying upfront that some of my understanding could be wrong as well. But I also need to feel that logically some of my arguments were inconsistent.
 
Hi res audio reminds me of Supertweeters that were in the market about ten years ago. They were as expensive as most speakers they were supposed to be added to, by placing them on top of any full range speaker and appropriately wiring them in.
When it was pointed out that the 30khz they supposedly reproduced had very little energy in most music, and was inaudible even if it did, the marketing spiel went as follows:
By taking away the load of trying to produce higher frequencies than the main speakers are capable of, the main speakers are left free to concentrate their efforts on what they are capable of doing, thereby improving the sound of the main speakers in the audible range, even if there is no audible output from the super tweeter.
Ingenious?:eek:hyeah:
They died a natural death. I think.
 
We are close enough, but save some clapping for a bit longer:).
You are now largely moving out of theory into practice.
But first, yes 96khz sampling rate will have frequencies up to 48khz. If there is any being produced with enough energy to be heard,even if human hearing were to reach those levels, which it doesn't.. And recorded of course, that is a valid point you have made too.
And for frequencies above 22khz, there is a steep rolloff on CD. No doubt. A but will follow later:).
By the way, how come you missed the 16 bit to 24 bit part of this saga?
Where I disagree with you in theory is this:
There is more sampling data at 20khz. But it doesn't add a jot of extra " value". If I already have a sample of all the necessary information why do I need more? There would be no use of that extra data up to 20khz for anyone, from bats to Superman to Mr Golden Ears Audiophile. It also doesn't add any value to the playback system.
There is one other thing to remember about 24/96. I don't know the theory, and I haven't the experience of this - I can only recount something I have read. With that upfront admission, it seems that 24/96 can, in some cases, actually introduce distortion of some kind in the frequencies upto 20Khz. In practice then, it can be a possible loss/no audible win situation.
Now, to the but I referred to earlier:
Other than the supposed distortion referred just above, all the theory about 24/96, even if 100% correct, means nothing - to me at any rate - if the difference between CD and Hi res cannot be distinguished in a level matched AB blind test.
The problem is that Hi res music is also often remastered with more care than the older CD, and usually this is done by the mastering studio A team. This remastering will sound audibly better, depending on how well it is done, and how lousy the original CD mastering was. To eliminate this variable, one needs to downsample the HD files to 16/44 or 16/48, and then still identify the differences in a rigourous listening test. If found, this is a validity of audible superiority of 24/96, mastering differences being eliminated. In the absence of audible benefits, this is poor engineering, being unnecessary use of resources.
Afaik, no one in the world has established such a difference in such a test.
By the way, you do know that people are talking about 24/384 now?

Well, Thad talked about xiph videos earlier. The first video kind of explains about higher sampling rate. I guess you will agree with it more than me explaining. Xiph.org: Video

Although, I have to say I agree with you. I don't know how that steep rolloff sounds like. Neither can I hear higher frequencies. But if there is more data for 20 khz frequencies, then better (my view). Because theory never says how many samples are needed to accurately predict the wave. This is because the wave is not exact sine wave. The Nyquist theorem says twice is the minimum, never mentions how much is sufficient.

About 16bit vs 24 bit, the xiph video explains that as well.
 
So you say that creation of sound is discrete, recording is discrete, and the way our brain detects sound is also discrete. So my original question was - why do you care if the sound wave was analog/continuous or not?
I care because that's what the truth is. But rather than admitting it was a misunderstanding, the whole argument is created around it with more and more analogies.
The original question was whether digital recordings can perfectly store music within our hearing range or not.
Don't get me wrong. I am in the digital camp. The only analog I have is the cassette deck and that's also because I have some cassettes from my college days. But it hardly gets used. Its there for sentimental reasons. :)
We see this all the time. Audiophile equipment manufacturers get into deep level physics and when someone makes a practical argument about how these physics principles are relevant, the standard strategy is to go even deeper into physics. I guess the strategy banks on the fact that most audio enthusiasts are not usually double PhDs in physics so when faced with esoteric physics, they will never be able to prove or disprove anything.
Yes, we just witnessed one here with sound wave not being continuous.
I have only studied a bit of physics but at least enough to hold a hopefully decent conversation. If you really want to get into a theoretical physics argument about the true nature of waves and the true nature of matter, there are layers upon layers of logic. Like I mentioned earlier, if you want to properly argue this, you can get down all the way to quantum mechanics - where all your smooth looking waves become discrete entities again.
I don't know how much physics I have studied, but I do read and try to understand. The analog to digital capture in this thread happens to be one such a topic and I tried to explain the way I understand it with visually. I know you said its wrong and but I haven't heard a different explanation from you other than quantum physics, discrete data, and non-continuous waves, with eardrums + stones in water + what not thrown in. Well, that's probably what you explained above.
The thing to note is that all these are mathematical and theoretical models. Meaning - that perfect looking sine wave? It is neither perfect in real life nor does it even look like Michael Jackson doing break dance.
Well, agree with you here. The ideal sound is sine wave, but not so in reality. But think for a second, won't we need more data to accurately reconstruct the imperfect actual wave? Again - I don't know what that number is.
Ultimately what matters is how we interact with these physical phenomena, namely sound. So if my ear hairs get vibrated 20 times a second for me to hear a 20hz note, and if a digital recording claims that it stored at least 40 samples of the original vibration, and can thus re vibrate my ear hairs 20 times a second when I press the play button, it makes sense to me that the digital recording is telling the truth. Whether the theory of relativity was involved in the wave being transmitted is irrelevant, at least for me. I only care that my ear hairs be re vibrated with the same level of accuracy when I heard the instruments being played live.

I will not be able to have a discussion with you if you are taking this discussion to a topic that is about the purity of the wave or not. I do not have that level of knowledge, honestly speaking.

And I was also saying upfront that some of my understanding could be wrong as well. But I also need to feel that logically some of my arguments were inconsistent.

Well, all I want is the meaningful discussion, devoid of digressions. There may be theories, and one doesn't need to know those theories for enjoying the music. We can ignore those. But we cannot dismiss those theories and how those are applied in a discussion and totally go around creating analogies. Nobody has to take my word for it. If someone says I am wrong, then explain it to me.

And no - I am not talking about purity cause I am not in that camp. All the music or sounds we hear are processed sound.
 
Well, Thad talked about xiph videos earlier. The first video kind of explains about higher sampling rate. I guess you will agree with it more than me explaining. Xiph.org: Video

Although, I have to say I agree with you. I don't know how that steep rolloff sounds like. Neither can I hear higher frequencies. But if there is more data for 20 khz frequencies, then better (my view). Because theory never says how many samples are needed to accurately predict the wave. This is because the wave is not exact sine wave. The Nyquist theorem says twice is the minimum, never mentions how much is sufficient.

About 16bit vs 24 bit, the xiph video explains that as well.
As to the theorem, it says that the twice is the minimum necessary to accurately reconstruct the wave - and leaves it at that. Perhaps a statement like that is easier to prove mathematically, than one that says it is sufficient - who know, it needs a math expert to say yes or no to this supposition?!
I interpret this to mean that 44100 times a second sampling in CDs is able to accurately reconstruct the waves of frequencies up to 20khz.
As to xiph, I am aware of the site for quite some time. But not having understood all they say very well, I don't refer to it often to others.
 
manoj.p said: :clapping::clapping::clapping:
The Nyquist theorem says twice is the minimum, never mentions how much is sufficient.

YES !

I was waiting when someone will point this out! ;)

The Nyquist theorem ASS-U-ME(S) that there are an infinite number of identical waves available to be sampled at atleast 2f so that the original waveform can be re-constructed faithfully.

It is VERY VERY Important to Always study and accomodate basic assumptions when using a theory. If the Basic assumptions do not apply, the theory too does not apply.

"Brick wall" filters with Very Very Sharp cut off filters ( 60dB per octave ) above +20Khz are required to prevent aliasing. Simplistic arguments about the ear's upper threshold ( ie frequency domain or from a frequency perspective) project these filters in good light.

But a Time Domain ( ie from a time perspective) analysis show GROSS distortions ! Believe it of not...., these filters actually have the reproduced sound starting BEFORE it should.....

Part knowledge is always dangerous....
 
As to the theorem, it says that the twice is the minimum necessary to accurately reconstruct the wave - and leaves it at that. Perhaps a statement like that is easier to prove mathematically, than one that says it is sufficient - who know, it needs a math expert to say yes or no to this supposition?!
I interpret this to mean that 44100 times a second sampling in CDs is able to accurately reconstruct the waves of frequencies up to 20khz.
As to xiph, I am aware of the site for quite some time. But not having understood all they say very well, I don't refer to it often to others.

Well, I referred that site because I thought it would get better reception than me. :D

Anyway the site talks about 44.1K vs 96k and that the filters beyond 20k are more gradual in 96k. About 8 bit 16 bit, it talks about clipping and reduced dyamics with examples of sounds. It's fast video with lots of technical words, but interesting presentations.
 
Guys, guys!

We were assembling some basic building blocks of understanding. Even if they might have looked purile to an actual engineer or mathematician, they were getting us somewhere.

Then it all went crazy about the nature of analogue sound, which is the least of our worries. Isn't it almost enough to say that noises happen, without going into any detail, let alone controversy, about how they happen? By the time those noises reach an ADC, they are at least one step away from sound in air: they have become electrical signals already. Some of them may never have been sound in air in the first place.

Manoj: how many points do we require to reconstruct a curve?

--- If it is an arc of a circle then I think it is three (assuming of course, we don't know its centre and radius!)

--- If it is compound curve, then it will depend on the curve

--- If it is a complex sound wave, then we need twice the highest frequency every second. Others have posted that already. Given that, we do not get a better, or more accurate, curve just by adding more samples. Whether we get a better, more accurate result from our DAC, because of the engineering involved in the filters, is indeed a different question. And whether any specific DAC product produces a more accurate sound with one sample rate (not necessarily the higher) than with another, is yet another product/engineering related question.
 
We were assembling some basic building blocks of understanding. Even if they might have looked purile to an actual engineer or mathematician, they were getting us somewhere.


Whether we get a better, more accurate result from our DAC, because of the engineering involved in the filters, is indeed a different question.
:). It is the nature of any internet forum - this one was more civilised than many!
You can't get a more accurate result from any DAC than what was converted by the ADC in the first place. It may sound better, due to more sound shaping filters, but that doesn't mean it is more accurate - indeed it would be less accurate.

On my part, I would say that the thread has fully met its desired purpose.
 
But a Time Domain ( ie from a time perspective) analysis show GROSS distortions ! Believe it of not...., these filters actually have the reproduced sound starting BEFORE it should.....

Part knowledge is always dangerous....

This is exactly what I stated earlier about pre ringing. The biggest issues in most dacs are with the analog reconstruction filters. A poorly designed traditional filter after the dac can do very serious harm to the sound.

Pretty much every good dac worth its salt uses a minimum phase (apodizing) filter these days to avoid pre ringing. DACs that still use traditional brickwall filters should be relegated to stone age.
 
Band limited signal sampling is not just a simple measurement of the wave for height (amplitude) or width (frequency). Sampling is done using a mathematical functions whose fourier transforms are zero outside of a finite region of frequencies, which is why the requirement for a band limiting. The regenerated waveform will be exactly as the input waveform irrespective of the frequency measure within the band range because it will be an unique solution. Multiple waveforms do not exist because they will not fulfill the sampling function.

I think Monty best explains it with demonstration in the below video

Xiph.Org Video Presentations: Digital Show & Tell

It is the compression/decompression and implementation of digital music which degrades the output.
 
ohmygod, you've mentioned Fourier transforms. I still have not learnt how to hear that and retain conciousness, yet alone understand it :lol:. I'd better watch the Monty video again, especilaly as I've telling everybody else to!

Sawyer, yes, it was pretty civilised ---and civil--- a few of us have been through a lot worse together on this very forum :eek:
 
Well, I will go and read those. But one question for quickly satiating my thrust. What that min no is to perfectly draw a wave? I have struggled to find an answer but looks like google has missed this one (or I have missed this one) And what if the original wave is not a pure sine wave?

Here is my take:

Given a set of points, there are infinite number of curves that fit those points. And also consider that reality need not be 3-dimensional, but multi-dimensional. But when we put limits/conditions - such as min of 20 hz and max of 20khz, then that number reduces, and hence representable in limited amount of information.
 
I think even aliasing is fairly misunderstood as well. Let me try and explain what it is.

When you are sampling within a range of frequencies, say 20 - 20k Hz, if your input audio contains a signal at 20KHz and 30Khz for example, then all three will result in the same value equating to that of 20Khz. When converted back to analogue this will create a second waveform called an alias.

There are 2 techniques to combat this.

You can store extra information and extrapolate the waveform to 30Hz approximately, but the problem is in identifying which is the original and which is the alias. Even if we did identify, extrapolation will result in a degraded audio signal.

Instead the easier approach is taken, since we can hear only between 20 and 20K Hz, a low-pass filter is used before the sampling function to keep all frequencies below 20Khz only. Considering the use of the low pass filter, in context it is called an anti-aliasing filter.

Hope this helps.
 
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