IndianEars
Well-Known Member
Well, then it could be argued that this thread does not exist at all ! 
Jest Kidding
Jest Kidding
Digital audio fundamental question
- Thread starter Sawyer
- Start date
Thad, Let me ask you a question about this. With 44100 sampling rate, what are the no of samples taken per wave for 20 hz, 200 hz, 2000 hz and 20000 hz?
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Useful link, if you have the time on hand to read it:
"Digital audio cannot possibly work!" (they say) ... marketing audio gear - Page 2
"Digital audio cannot possibly work!" (they say) ... marketing audio gear - Page 2
vikoma
Member
All I am trying to point out is that when limited set of bits have to represent something analog, is it theoretically one-on-one equivalent or not. It can indeed be one-on-one if we put some conditions on what we want to represent.
For example, 1/3 is 0.33333..., and seems infinite, and is not representable in digital. But we can represent as tuple (1, 3) without loss of information. In contrast, pi (3.1415...) is indeed NOT representable in digital because it is an infinite series.
Is world fundamentally digital or analog? Going by quantum theory, it is definitely digital. (As an aside, I am sure most have seen the movie "The Matrix", where reality is simulated in digital computer.)
If it is all digital out there, any analog we see, at a very deep down level, is ultimately digital. If so, then we want to be able to ask: Is an analog signal, by its very nature infinite and hence never representable in digital? (like pi)?
To simplify, is a sine wave representable in digital without loss of information? Is Nyquist/Shannon theorem of sampling an approximation only or one to one equivalent?
All I am saying is that it is indeed one-to-one equivalent only when you put bounds on lower and higher frequencies . Hence, there is no loss of information in digital.
Conveniently for us, it just so happens that our ears only recognize only limited range, and hence we are able to leverage the theory and enjoy analog-equivalent music in digital.
Thad E Ginathom
Well-Known Member
How would that matter*?
I'm not clever enough to work that out (reminder: I was thrown out of maths class at 15) but I don't believe it matters. We get the music. The wave form
But, as others have said, this has not been a straight plug-and-play transition of theorem to practice, but one with many engineering challenges which are continuing to this day.
*Take a look at this presentation by jj Johnston. Some of it is relevant to this thread, and all of it is interesting. (When he talks about the ear/brain feedback mechanisms, bear in mind that this is one of the guys who invented and developed MP3, and, whether we like/use lossy compression or not, it could not be developed without extraordinary expertise in the mechanisms of audio perception). IIRC, there is some point there where he talks about being taken by surprise, at some point in the digital-music-development histroy, that some frequencies were working, and others were not. To be honest, I don't remember clearly, but it is a good video, worth an an hour of our time, even if I have got that bit wrong.
It does matter Thad. If you think that sampling rate more than double is actually harmful.
To answer the question. Since the sampling rate is constant, you will have 1000 times samples for 20 hz frequency compared to 20Khz. At 20 hz, we will have 2205 samples compared to 2.205 samples at 20Khz. As per the notion that more than double sampling rate actually harms - we should have had very harmful effect below 22050 frequency because all the below frequencies get more than double sampling rate for those individual frequencies.
And the audio wave is a perfect sine wave in a perfect world. But we aren't living in perfect world, are we? The audio wave in reality is quite different than the sine wave. It would be easy to construct a perfect sine wave with less sample but it wont be real life.
By the way - DSD is the format used for archiving analog tape. It's 1 bit audio but sampled at 64 times of 44100. The 1 bit is very low resolution compared to 16 bit of CD. Go figure.
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Thad E Ginathom
Well-Known Member
It's not that I do necessarily... see the Xiph articles. When it is in a bad mood, I do get aliasing on my sysem. I have no clue why it is only occasional. I'm glad
A sine wave is abut the representation of a certain kind of tone. It also (in ways that are beyond my understanding) seems to be a very basic building block of all sound. It is not about perfect worlds. Apparently, if you are listening to music right now, you are listening to sine waves right now. Is the world perfect?
(well, I hope your music is making your world perfect for you
)DSD is something that I have barely begun to get my head around yet, but have a vague clue that it works not by saying "what is the value of the number in this sample," but by seeing how many times a bit switches its value. Resolution is not really a digital-audio term, it is a digital visual term which audio sales people like to use because audiophiles like it, but it is not like if 24 bit is better than 16 bit is better than ...duh? 1 bit is best? Counter-intuitive stuff again, I suppose. Presently, this part of the subjects beats me entirely!
It's not that I do necessarily... see the Xiph articles. When it is in a bad mood, I do get aliasing on my sysem. I have no clue why it is only occasional. I'm glad
A sine wave is abut the representation of a certain kind of tone. It also (in ways that are beyond my understanding) seems to be a very basic building block of all sound. It is not about perfect worlds. Apparently, if you are listening to music right now, you are listening to sine waves right now. Is the world perfect?
(well, I hope your music is making your world perfect for you
DSD is something that I have barely begun to get my head around yet, but have a vague clue that it works not by saying "what is the value of the number in this sample," but by seeing how many times a bit switches its value. Resolution is not really a digital-audio term, it is a digital visual term which audio sales people like to use because audiophiles like it, but it is not like if 24 bit is better than 16 bit is better than ...duh? 1 bit is best? Counter-intuitive stuff again, I suppose. Presently, this part of the subjects beats me entirely!
Thad, I have read the Xiph article. All I got from there that 96 Khz and more could be bad. I can send you link to another articles that say otherwise. Here is one for starters. Tech Talk 3: All About Sampling
Thad E Ginathom
Well-Known Member
Oh, Manoj, I've just addled my brain trying to take in this one!
Sampling Theory for Digital Audio - Dan Lavry
If you can stand another dose, take a look. I'm going to have to call it a day on trying to digest this stuff. This paper goes much more into the maths of DA/AD. I believe, by the way, that Dan Lavry designs his own DACs --- as in does not buy in other people's chips for the ADCs and DACs that he sells.
By the way, I've read JJ Johnston assert that about 60Kh would be optimum. Lavry says much the same, but, given the rates that the industry offers, is prepared to settle for 96khz. As far as I can understand it, that is not to give people extra content that they can actually hear, or that affects them in some way, but it is because it makes the entire conversion/filtering path better. It is interesting that the word "optimum" is used, which is something that some in this thread have been looking for. So, increasing is better up to a point, but not better after that point.
See you tomorrow
Sampling Theory for Digital Audio - Dan Lavry
If you can stand another dose, take a look. I'm going to have to call it a day on trying to digest this stuff
. This paper goes much more into the maths of DA/AD. I believe, by the way, that Dan Lavry designs his own DACs --- as in does not buy in other people's chips for the ADCs and DACs that he sells. By the way, I've read JJ Johnston assert that about 60Kh would be optimum. Lavry says much the same, but, given the rates that the industry offers, is prepared to settle for 96khz. As far as I can understand it, that is not to give people extra content that they can actually hear, or that affects them in some way, but it is because it makes the entire conversion/filtering path better. It is interesting that the word "optimum" is used, which is something that some in this thread have been looking for. So, increasing is better up to a point, but not better after that point.
See you tomorrow
It's not that I do necessarily... see the Xiph articles. When it is in a bad mood, I do get aliasing on my sysem. I have no clue why it is only occasional. I'm glad
A sine wave is abut the representation of a certain kind of tone. It also (in ways that are beyond my understanding) seems to be a very basic building block of all sound. It is not about perfect worlds. Apparently, if you are listening to music right now, you are listening to sine waves right now. Is the world perfect?
(well, I hope your music is making your world perfect for you
DSD is something that I have barely begun to get my head around yet, but have a vague clue that it works not by saying "what is the value of the number in this sample," but by seeing how many times a bit switches its value. Resolution is not really a digital-audio term, it is a digital visual term which audio sales people like to use because audiophiles like it, but it is not like if 24 bit is better than 16 bit is better than ...duh? 1 bit is best? Counter-intuitive stuff again, I suppose. Presently, this part of the subjects beats me entirely!
Thad, a small correction. The frequency of the sine wave is the representation of a certain tone we hear. It could have been a triangular wave for all that matters. The 50hz tone we hear is caused by 50 little bursts of air in a second triggering our ear hair.
It is the equivalent of strumming a guitar string 50 times a second. Does it matter if we used a finger nail or a plastic pick? The nature of the wave is a red herring.
In my limited knowledge, oversampling is done to compensate for the engineering limitations, not the theoretical limitations (which are none)
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Good time to ask this:
If one was to use a tuning fork vibrating under the influence of a steady impulse, with a frequency of 1 unit and amplitude of 1 unit, that is all one needs to know to have the fork reproduce an identical vibration/sound from a digital recording of that impulse using Nyquist.
Representing this as a sound wave on paper, where both axes have the same scale for each unit, one just has to plot the data points as dots, and then connect the dots via straight lines. No other information is needed to do this, there is only one way to join two dots using straight lines.
Why then are curved lines used? These mislead people into thinking that more information is needed to plot the curves, and the more the information, the closer one gets to the actual curve.
PS: To digress, reading about reality and quantum mechanics here reminded to re read a book on the subject that I had read a long time ago. The Dancing Wu Li masters by Gary Zukav. An entire book on the subject with no mathematics in it! Highly recommended From there I read many books on this very fascinating subject, the most recent one being The Elegant Universe, Brian Green. M theory, strings, super strings, Cosmic level black holes and basic particles having mathematical equivalencies and much more. Apart from some very small parts, the arguments and explanations in it sailed over my head with lots of room to spare.
Thad E Ginathom
Well-Known Member
I don't understand what you are getting at? Nyquist doesn't have anything to do with tuning forks or any sound in analogue domain, ie any sound other than digital sound.
Why a curve? Because it is a curve. If you find one of those diagrams of sound in air, showing the compression/decompression of the air molecules, you can see that it is a continuous change from one to the other.
Forget Nyquist for this. My question is that if the frequency and amplitude data points I referred to for the tuning fork earlier are plotted on a paper, and joined by straight lines, will this be an wrong representation?
And if the right representation is a curve, can it be drawn in exactly the same way each time using just those data points?
This is one aspect I am still fuzzy about. Correct that, I am fuzzy about lots more on digital audio, but this is something I would like to straighten out in my head. Rest can remain in ignorance is bliss domain.
Thad E Ginathom
Well-Known Member
Yes. A square wave does not sound the same as a sine wave.
Time for you to go play with synthesiser software, or even an audio editor like Audacity
Consider the springy strip analogy in my first post in this thread: it will always follow the same curve.
Now look at the paper by Dan Lavry (my post last night), which has some very pretty graphs (although they still make my brain hurt) showing how actual maths is used rather than a springy strip.
Me too! :lol:
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For simplicities sake, let stay with a tuning fork, vibrating at the same frequency and amplitude for a fixed time period of say 1 minute. All that can be picked up for this fork as data points is amplitude and frequency? Which will be the same for the entire minute?Yes. A square wave does not sound the same as a sine wave.
Time for you to go play with synthesiser software, or even an audio editor like Audacity
Thad E Ginathom
Well-Known Member
Time for you to go play with synthesiser software, or even an audio editor like Audacity and a microphone :lol:
OK, I've never done such experiments as comparing wave shape from different sources, but I'm sure it would be good to help realise these things!
Of course... a tuning fork always vibrates at the same frequency, otherwise it would be sacked as a tuning fork ...but not the same amplitude. We need an electronic source for that.
OK, I've never done such experiments as comparing wave shape from different sources, but I'm sure it would be good to help realise these things!
Of course... a tuning fork always vibrates at the same frequency, otherwise it would be sacked as a tuning fork ...but not the same amplitude. We need an electronic source for that.
To continue with this line of exploration, I think I can safely assume the answer to the above to be yes, to both.
Here is where it gets into unknown areas for me, staying just with the tuning fork because I have a slow intellect.
If just joining these data points by straight lines results in an incorrect representation of the sound the tuning fork is making, why is that the case? I use straight lines just because even I understand that to draw a straight line connecting two points doesn't need any more information. My reasoning tells me that drawing anything else, does. Or am I wrong here? I don't know what a sine wave is other than what it looks like in general terms - is it the case that there is only one possible sine wave that can be drawn to connect the data points of constant amplitude and constant frequency?
PS: Assume here that the tuning fork has the same amplitude because of an external energy source.
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Hi Sawyer,
From what (little) I have read and understood, the reason why a sine wave is used is because it is the literal and accurate representation of the way energy propogates.
However, we make the mistake that this is also the way our ears understand or receive sound. Our ears get triggered by discrete pulses and yes, you are right, they only care about the frequency and amplitude (strength) of these pulses, not about how the energy waxes and wanes in a sinusoidal manner.
To your other point, I would love to read The Dancing Wu Li Masters. I loved the Tao Of Physics which I read many years ago, and it was quite a profound experience for me.
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