Digital audio fundamental question

[Hari655]

Just my opinion.

My opinion Digital should not have any loss.

If that is the case...IMAX,CINIMAX and new multiplex business would be closed.

If digital has loss then how come the digital era has much better video clarity and graphics.

Another thing...

Either Digital or Analogue end of the day...both regulate current and put up the show...so what ever it is end of the day everything manipulation of current.

I may be 1000000% wrong but i am ready to understand if my thinking is wrong.

Forums = Opinions and just opinions and everything is learning.

Thanks,
Yashwanth

 

[jls001]

4200 - Conversion Principles - Sampling

The next chapter is also very interesting: 4200 - Conversion Principles - Quantization

 

[Thad E Ginathom]

Just my opinion.

My opinion Digital should not have any loss.

If that is the case...IMAX,CINIMAX and new multiplex business would be closed.

If digital has loss then how come the digital era has much better video clarity and graphics.

Another thing...

Either Digital or Analogue end of the day...both regulate current and put up the show...so what ever it is end of the day everything manipulation of current.

I may be 1000000% wrong but i am ready to understand if my thinking is wrong.

I think that digital visual and digital audio work in different ways, and that it is dangerous to try to talk about both at the same time.

 

[asliarun]

One thing to note (from the article Sawyer posted) is that anti-aliasing is caused because of an engineering limitation - where your samples are capturing information about frequencies that are outside the Nyquist limit.

If you can give a perfectly band-limited frequency range of audio sound - 0 - 20KHz, say, you are using playing a bunch of instruments in an anechoic chamber, and none of the patrons have ultrasonic ringtones (of course, the phones are not on silent mode!), you will never encounter the problem of anti-aliasing.

The reason why I find the sampling diagram (so commonly used) so misleading is because we mentally tend to jump from the analog sample example to doing the same thing for a sine wave.

Remember, an entire sine wave (which is just a mathematical representation anyway) - i.e. peak to peak, or trough to trough - represents one single wavelength.

In the analog signal (the one that looks like a misshapen waveform), remember, each change or "jag" that causes the misshape is equivalent to one full wavelength of the mathematical sine wave. The most fine-grained or nuanced change in the analog waveform will be at most 1.7cm in length (or 1/20000 second in duration) for 20Khz. If you would draw that specific example in graph paper, you would draw it as a full sine wave, where the distance between peak to peak would be 1.7cm. (Which is why I said earlier that only the peaks are important - for the sine wave representation, not the analog wave!

And since we sample the analog wavelength at an even faster rate (we sample every 0.85cm or once every 1/40000 second), we will always be able to reproduce the analog waveform. Again, remember, any change in the analog waveform that is shorter than 1.7cm (greater than 20Khz) is considered to "not exist" as far as our problem statement is concerned. That is why the big upfront caveat about band-limiting the analog signal to 20KHz (1.7cm).

And just to be clear, if you are listening to live music where everyone is singing or playing normal instruments, and assuming none of those instruments can go higher than 20KHz, the analog wave (music) they will produce - will *never* have a change or "jag" that is less than 1.7cm. in length. Which is why we confidently state that our digital samples are perfect in every sense of the word.

Now, how fine-grained reality (and any arbitrary analog sound wave) really is - is an academic question. Depends on the "zoom level" of our senses I guess. But do we lose visual fidelity for example, if we cannot see individual atoms in an image?

But regardless, we have to put this issue to rest that a digital audio signal is somehow imperfect because it has holes or whatever. Or that audio somehow escapes the basic principles of Nyquist.

 

[Thad E Ginathom]

Guys... One of the main reasons for digital misunderstanding seems to be in the interpretation of the word "sampling."

If I go to a buffet and only sample each of the dishes, then I leave most of the food uneaten. If a music companies sned me samples from their catalogue, then I get songs and excerpts, not whole albums. This is what I consider the normal, everyday meaning of the word. But we are talking about stuff which comes from high maths, and I am wondering if a sample to a mathematician is different to sample to a shopper?

I was thrown out of the maths class at 15. I have no clue. But someone here will...



(Arun, do you do this stuff for a living? You are very good at explaining it. Consider yourself added to my list of teachers.)

(Do I have to call you guruji now? hyeah: )

 

[Sawyer]

But regardless, we have to put this issue to rest that a digital audio signal is somehow imperfect because it has holes or whatever. Or that audio somehow escapes the basic principles of Nyquist.

As far as I am concerned, I see no issue anymore, even in theory - in practice, as I have said earlier, I wasn't seeing any that were not in the mastering to begin with.

Implementation issues which troubled early digital solutions have now been solved to the extent audible, and the solutions have by now filtered down to budget digital audio equipment too - leaving mastering, speakers and room acoustics to reign supreme as the problem areas. People selling USD 70K DACs will keep talking about gaps and art v science, but it is all irrelevant to me if I cannot hear their efforts in a precision level matched AB blind test, with just a single variable changing. I am referring to the pure DAC component, not the sound shaping filters that many DACs employ. That is the realm of DSP/room EQ, and another subject, though very relevant to the home audio experience.

Mastering issues remain even today. To a large extent, we remain at the mercy of what happens there. It isn't an engineering problem, that.

 

[Sawyer]

I am wondering if a sample to a mathematician is different to sample to a shopper?

Not really. It is more language than math. Think of sample size as 100% of the relevant universe. Or a map drawn to a scale of 1:1.

 

[Sawyer]

(Arun, do you do this stuff for a living? You are very good at explaining it. Consider yourself added to my list of teachers.)

+1 to that.
And although I am not an engineer, I have a lot of respect for the discipline and its practitioners. This learning has raised that respect by another notch.

 

[Sawyer]

My next to do is something that Arun pointed me to as well - the DSpeaker Room EQ box. The Indian distributor in Mumbai has sent one to Pune for a home audition over a couple of days. Interesting times ahead.

 

[manoj.p]

No they don't.

That is the number-one biggest misconception of digital music. This has nothing to do with ears, belief, faith, or what format we choose to buy our music in, it is simple science. Simple science that, as I said, I for one only became aware of amazingly recently in my long[ish] life.

More samples do not give a better, or more accurate, waveform. The do give the possibility of a bigger frequency range, and whether that is better or not is another issue entirely.

Please consult the science on this: it is there all over the web, and not too hard to find, but we have to be able to accept the counter-intuitive on this. "common" sense does not help: more samples does not leave less out!

Will try to catch up with the rest of the thread later, have to go out now

Well, it does give the possibility of bigger frequency range, upto half of sampling frequency.

But its also a fact that more samples give better wave form. We know that the wave may not be perfect sine wave, so more samples means accurate waveform and less guess work. You can do this experiment. Using pencil,draw a wave. Then take 4 points on the wave, at regular interval. Erase the wave, leaving points on paper. Ask someone else to make a wave out of it.
Now, on another paper, draw one more wave. Now, take 16 points similar to above, erase the wave. Give this paper to that person. And now tell me which waveform is closer to original.

Also, one thing to remember is that sampling frequency does not change from one frequency to another. So, if we were to take 44100 samples per sec, it will take about 2 samples for 22050 frequency. But at 4410 frequency, it will take 5 samples. Another thing is that since the sampling is done for all the frequencies at once, not all the samples will denote peaks for each frequency. Some may be peaks, some may be while rising, some while declining, some on trough part. So, its always better to bit more samples.

Again - double samples are min, but more will take guesswork out.

 

[Sawyer]

But its also a fact that more samples give better wave form. We know that the wave may not be perfect sine wave, so more samples means accurate waveform and less guess work. You can do this experiment. Using pencil,draw a wave. Then take 4 points on the wave, at regular interval. Erase the wave, leaving points on paper. Ask someone else to make a wave out of it.
Now, on another paper, draw one more wave. Now, take 16 points similar to above, erase the wave. Give this paper to that person. And now tell me which waveform is closer to original.

24 hours ago, I was in the exact same place as you are. There are better teachers than me here, so I will wait for them to chip in.
I will leave you with just one thought - there is no wave of the kind you describe! Just vibrations.

 

[manoj.p]

24 hours ago, I was in the exact same place as you are. There are better teachers than me here, so I will wait for them to chip in.
I will leave you with just one thought - there is no wave of the kind you describe! Just vibrations.

Yes, I think I should just give up here.

But I can't resist one question - How are those vibrations transmitted through air?

 

[Sawyer]

Yes, I think I should just give up here.

But I can't resist one question - How are those vibrations transmitted through air?

No, don't give up...folks here are patient enough.
As to your question - via air molecules passing the vibrations on to the adjacent ones, on the other side of the ones that passed it on to them. Which is why sound does not travel through a vacuum, unlike light. The classic tuning fork vibration diagram shows this well.

 

[asliarun]

Well, it does give the possibility of bigger frequency range, upto half of sampling frequency.

But its also a fact that more samples give better wave form. We know that the wave may not be perfect sine wave, so more samples means accurate waveform and less guess work. You can do this experiment. Using pencil,draw a wave. Then take 4 points on the wave, at regular interval. Erase the wave, leaving points on paper. Ask someone else to make a wave out of it.
Now, on another paper, draw one more wave. Now, take 16 points similar to above, erase the wave. Give this paper to that person. And now tell me which waveform is closer to original.

What you are failing to note is that with peak humn hearing ability, you cannot have the analog wave change in between your 4 samples. So even if you sample 16 times, you cannot draw the original wave better because the original sound wave is only a sequential collection of tones. And sequential means discrete, not continuous. And our samples are taken at a higher rate than the transitions in the analog wave.

Real world is discrete not continuous. The word "quantum" in quantum mechanics, which is how the world works at a zoom factor of one million, literally means "discrete" or non-continuous.

Quantum
physics : the smallest amount of many forms of energy (such as light)
2a : any of the very small increments or parcels into which many forms of energy are subdivided

Also, one thing to remember is that sampling frequency does not change from one frequency to another. So, if we were to take 44100 samples per sec, it will take about 2 samples for 22050 frequency. But at 4410 frequency, it will take 5 samples. Another thing is that since the sampling is done for all the frequencies at once, not all the samples will denote peaks for each frequency. Some may be peaks, some may be while rising, some while declining, some on trough part. So, its always better to bit more samples.

If that were the case, how does a gramaphone record reproduce multiple frequencies? All it does is trace a single path that has been carved into the groove of a circular record.

Again, the answer is that sound that you hear is a set of sequential transitions of waves. Heck, we only have one eardrum (in each ear) that can only vibrate once at a given point in time. That is why we like stereo so much because it lets us hear differently with both our ears!

On a side note, I have always wondered if things like soundstage is really just a system being very good at stereo (and the brain having a gala time creating this illusion in our head because it finally hears different from both ears!). So maybe I should look for a stereo amp that is really good at channel separation and has minimal crosstalk between the channels??

Thad and Sawyer, glad you liked my explanations. But please, I am not a teacher or guru! Am a software engineer by profession and try to make a little sense of the world around us. And my mind perpetually balks at the level of abstraction that surrounds us nowadays so I try to translate these things in ways I can understand. And this is so ironic because software is all about abstraction!

 

[manoj.p]

No, don't give up...folks here are patient enough.
As to your question - via air molecules passing the vibrations on to the adjacent ones, on the other side of the ones that passed it on to them. Which is why sound does not travel through a vacuum, unlike light. The classic tuning fork vibration diagram shows this well.

And what that motion would look like, if we could actually see those air molecules?

 

[Sawyer]

Real world is discrete not continuous. The word "quantum" in quantum mechanics, which is how the world works at a zoom factor of one million, literally means "discrete" or non-continuous.


On a side note, I have always wondered if things like soundstage is really just a system being very good at stereo (and the brain having a gala time creating this illusion in our head because it finally hears different from both ears!). So maybe I should look for a stereo amp that is really good at channel separation and has minimal crosstalk between the channels??

Thad and Sawyer, glad you liked my explanations. But please, I am not a teacher or guru! Am a software engineer by profession

Digressing in the reply:
Reality is Digital - that's one in the eye for the analogue fans:lol:
But, knowing from my readings of modern physics, it may not be that simple. Wave and particle both exist simultaneously. Or neither exist. And all matter is just energy vibrating at a different frequency. Thankfully, sound is a lot simpler than electro magnetic stuff. At least it is something that the human brain can conceptualise.

As to soundstage - it starts with the recording and mastering. Yes, amps need to have minimal cross talk, but this is not as critical.
Speaker placement, where you sit in relation to that, and the room acoustic play a big part in the illusion that the brain is able to come up with to give the effect of sound on a stage.

And the fact that you are an engineer gives you a big advantage over some of us that aren't. Our fundamentals tend to be hazy, and often a little knowledge can be more dangerous than none.

 

[Sawyer]

And what that motion would look like, if we could actually see those air molecules?

Not being funny...it would look like air molecules vibrating! In a direction away from the source that is. And vibrating less and less as the vibration is transferred from one molecule to the adjacent one.

 

[manoj.p]

What you are failing to note is that with peak humn hearing ability, you cannot have the analog wave change in between your 4 samples. So even if you sample 16 times, you cannot draw the original wave better because the original sound wave is only a sequential collection of tones. And sequential means discrete, not continuous. And our samples are taken at a higher rate than the transitions in the analog wave.

yes, agree with the part that the analog wave can't change. But let's assume the four point data given to one is not on peaks but at different locations. You would still have difficulty drawing it.

And whether we like it or not, the lower frequencies are getting sampled at higher rate. A 20Hz frequency is getting sampled at 2205. That's how much data is there. Now, I am not a DAC designer, so can't say if the conversion software throws out all that data and uses only 4 samples out of it. But that doesn't seem likely.

Real world is discrete not continuous. The word "quantum" in quantum mechanics, which is how the world works at a zoom factor of one million, literally means "discrete" or non-continuous.

Quantum
physics : the smallest amount of many forms of energy (such as light)
2a : any of the very small increments or parcels into which many forms of energy are subdivided

Not sure how this matters to the discussions at hand. I am not good at digressing into other things, but seems like this is going opposite to what you said above. First you said wave can't change, meaning its continuous. Now you say its discrete and non-continuous. If its not continuous, then we should have more discrete data, no?

If that were the case, how does a gramaphone record reproduce multiple frequencies? All it does is trace a single path that has been carved into the groove of a circular record.

even if there is one groove, the groove is made with various depths. Are you trying to say that its not possible to put all the frequency data together in one groove?

Again, the answer is that sound that you hear is a set of sequential transitions of waves. Heck, we only have one eardrum (in each ear) that can only vibrate once at a given point in time. That is why we like stereo so much because it lets us hear differently with both our ears!

Nice write up, but I don't understand what this has to do with discussion at hand. Sound existed before digital, before analog or any electronics was invented. And eardrum may vibrate once at any given point, but it can vibrate many times over, almost 15000 times in a sec. Brain just pieces that information together for us. Same way, a speaker can produce so many frequencies, even though its vibrating once at any given time. But we hear it all together. Our eyes do the same thing. We know all this - but what does it have to do with sampling rate in digital?

 

[rsud]

I'm avoiding any discussion of which is best. We have and will continue to have, lots of those

There is also some thought that all music is sine waves. ok... lots of them, added together, but still, sine waves.

I would disagree with this because a sine wave is supposed "perfect" or exact in frequency and amplitude over time. No non-electronic musical instrument is such. A bow across a violin is producing varying frequencies from the complex string and bow interaction along with harmonic resonances from the body of the violin, etc that would not deconstruct to the "perfect" sine wave for perhaps not even more than one cycle of the wave.

 

[manoj.p]

Not being funny...it would look like air molecules vibrating! In a direction away from the source that is. And vibrating less and less as the vibration is transferred from one molecule to the adjacent one.

And please bear with me and more questions. how does a vibration look like? Lets say, if I have a thin steel rod, upright and joined at bottom. If I push on the top very slightly, how the top of bar move during vibration?

I am using steel bar here for better visualization, but the vibration will be very same in the air molecules too.