Sampling rates and street sense. or when is close, close enough?

[Gregadd]

http://www.lavryengineering.com/forum_images/Digital_Audio.pdf

 

[amirm]

Other than needing a good spell/grammar checker like my posts , it is a good read to understand why digital "works."

 

[The Smokester]

Actually, I took from it why digital doesn't work. How can we read (and understand) the same thing and come to different conclusions?

 

[amirm]

The company makes digital audio products so it would be quite foolish to write a paper saying digital doesn't work .

You are right though that it starts of showing why digital may not work. But then he goes on to describe why the magic of Nyquist makes it work. That part gets a bit dense though so perhaps he was not so successful in simplifying that aspect.

 

[Gregadd]

Of course it wrks. We put a CD in and it plays something akin to music. The issue is how well it works. We can see what a a real music wave looks like. A lot more complex to sample and come up with an exact replica.

I recall in calculus we had to plot our own curve and try to empirically find dy/dx. We did not have a computer or those graphing calculators. It looked pretty ragged.

It does beg the question. Is sampling rate digitals' problem? Myself included, the long held belief by audiophiles.










http://interactive.usc.edu/members/adiab/Sine2xWave.jpg

 

[amirm]

Poor guy wrote a whole article to explain why the layman assumption of digital wrong and after reading it, your conclusions are the very thing he tried to address .

So let me help him along: Digital in theory is perfect. Let me repeat that again, in theory, digital is perfect and the math can show that to be the case.

The graph you show only serves to confuse you . The reason digital works is the principal that the signal must be band-limited. Sharp jaggies in a waveform mean high frequency detail. If that high frequency detail exceeds the digital system bandwidth then it cannot be represented. Fortunately, audio has pretty low bandwidth so making sure all of its frequencies fit in the spectrum of digital systems is not hard.

Your graph btw, is quite misleading. Look at the X axis. It is in seconds. In each one of those, there will 44,100 digital samples! Quite a few dots to connect the lines so to speak. Expand the graph to show the individual samples and you see that it is anything but jaggy.

There really is no smoke here guys. The theory is solid as a rock. If you doubt that, they you should doubt things like gravity .

If you want to attack digital, you need to attack its implementation in real life, not its theory that somehow those dots don't represent real signal. Here are the potential problem areas for digital:

1. Sampling theory assumes infinite sample resolution. If samples are limited in resolution, then you get what is called quantization noise. This can be dealt with using different math but is not explained way using Nyquist.

2. Sampling theory assumes that the timing of samples in both capture and playback match perfectly. This can be approximated pretty closely in a studio, but not necessarily so when a disc is shipped to you and you play it at home without connection to the same timing signal.

3. Sampling theory assumes that the Analog to Digital (ADC) and Digital to Analog (DAC) are perfect. The former is able to translate an analog voltage to its exact digital counterpart and the other does the reverse. That is not true in real life no matter how close we can come to perfection. Taking 1.4 volt signal and dividing it by 64,536 makes for very small increments.

4. Sampling theory requires that the source signal and output (reconstructed) voltage are perfectly filtered to match the sampling rate requirements. In real life, perfect filters are hard to come by.

So as you see, there are areas to attack . But the math is not it....

 

[Gregadd]

poor guy wrote a whole article to explain why the layman assumption of digital wrong and after reading it, your conclusions are the very thing he tried to address .

You will concede that the argument about inadequate sampling rates has been around for decades and not started by me. In fact products are made and sold based on that assumption.

So let me help him along: digital in theory is perfect. let me repeat that again, in theory, digital is perfect and the math can show that to be the case.

It is unlikely you will get converts on the first day of class.

The graph you show only serves to confuse you . I understand the difference between teaching examples and real world occurrences. The graph was plucked from the internet at random. The reason digital works is the principal that the signal must be band-limited. Sharp jaggies in a waveform mean high frequency detail. If that high frequency detail exceeds the digital system bandwidth then it cannot be represented. Fortunately, audio has pretty low bandwidth so making sure all of its frequencies fit in the spectrum of digital systems is not hard.

Your graph btw, is quite misleading. Look at the x axis. It is in seconds. In each one of those, there will 44,100 digital samples! Quite a few dots to connect the lines so to speak. Expand the graph to show the individual samples and you see that it is anything but jaggy.

I see graphs like that all the time. There is a difference between misleading and not supporting your theory. Indeed a graph of a full orchestra is even more complex.

There really is no smoke here guys. The theory is solid as a rock. If you doubt that, they you should doubt things like gravity .

So what is the ideal sampling rate if there is such a thing? Or does it even matter?
The paper suggests twice the bandwith.

If you want to attack digital, you need to attack its implementation in real life, not its theory that somehow those dots don't represent real signal. Here are the potential problem areas for digital:
I do no want to attack digital. Digital has come for me. The likelihood is that despite the analog renaissance evetually all music will be digital. Your work helped that happen.
1. Sampling theory assumes infinite sample resolution. If samples are limited in resolution, then you get what is called quantization noise. This can be dealt with using different math but is not explained way using nyquist.

2. Sampling theory assumes that the timing of samples in both capture and playback match perfectly. This can be approximated pretty closely in a studio, but not necessarily so when a disc is shipped to you and you play it at home without connection to the same timing signal.
Same problem with vinyl.

3. Sampling theory assumes that the analog to digital (adc) and digital to analog (dac) are perfect. The former is able to translate an analog voltage to its exact digital counterpart and the other does the reverse. That is not true in real life no matter how close we can come to perfection. Taking 1.4 volt signal and dividing it by 64,536 makes for very small increments.
Allow me to state the obvious-nothing is perfect. How audible is that?

4. Sampling theory requires that the source signal and output (reconstructed) voltage are perfectly filtered to match the sampling rate requirements. In real life, perfect filters are hard to come by.

I am sure you scientist will solve that problem.

So as you see, there are areas to attack . But the math is not it....

Again no desire to attack. Just examining the problems..

Thanks for your help. I'll be back after I have done more homework.

 

[Ron Party]

Amir, great post. The next question is, in an examination of the implementation, when does it fall short of the theory for us humans, i.e., when is that shortage audible, if at all. Related to that question is: how do we go about detecting any potential audible shortage. BTW, check your PM in about 5 minutes.

 

[Gregadd]

Do you need more dots for better accuracy?

http://www.lavryengineering.com/documents/Sampling_Theory.pdf

A little harder to digest.

 

[amirm]

I can only explain my own personal experience Ron. I can't represent all equipment or all people. Nor is my testing scientific enough to become solid evidence.

But in my careful blind testing, I find differences between digital transports, between transports with their video and display on/off, between high resolution formats such as SACD and DVD-A and between CD version of the same. I also find that better designed equipment in many cases outperforms mass market equipment. I also find standard PC audio to be very subpart of the box (many ship with resampling to 48Khz turned on by default!). Digital audio reproduction in my opinion then, lends itself nicely to high-end treatment in the hands of skilled engineers.

The differences I hear match the theory as I understand it. But how strong that cause and effect is, is hard to know absolutely.

I should not that the difference I hear is subtle and small. It is audible occasionally and requires focus, listening at louder than normal levels and usually through headphones. Because of that, I don't lose sleep listening to less than perfect setup. If the music itself is great, I still enjoy it immensely. When I have more time I will describe the differences I hear.

 

[Phelonious Ponk]

Amir, you are a very reasonable man with reasonable priorities.

P

 

[JackD201]

Amir,

So bit depth determines the total number and the size of voltage increments while sampling determines the bandwidth right?

If I got that right then it isn't just sampling but both to make digital better. There's something I don't get though. So here's my question. We know that the higher the bit rate the higher the dynamic range. Do the increments stay the same or more precisely, do the increments up to 96dB remain the same or do they get smaller when the bit depth is increased?

Thanks in advance!

Jack

 

[The Smokester]

The company makes digital audio products so it would be quite foolish to write a paper saying digital doesn't work .

You are right though that it starts of showing why digital may not work. But then he goes on to describe why the magic of Nyquist makes it work. That part gets a bit dense though so perhaps he was not so successful in simplifying that aspect.

Yes, amirm. I was just being snarky. Basically a sophmore's lesson in Nyquist. I don't think 44 kHz/16 bit is enough and also, there is the issue filtering, quantization and jitter which he doesn't address. I like your writeups better.

 

[The Smokester]

......The theory is solid as a rock. If you doubt that, they you should doubt things like gravity .

If you want to attack digital, you need to attack its implementation in real life, not its theory that somehow those dots don't represent real signal. Here are the potential problem areas for digital:

1. Sampling theory assumes infinite sample resolution. If samples are limited in resolution, then you get what is called quantization noise. This can be dealt with using different math but is not explained way using Nyquist.

2. Sampling theory assumes that the timing of samples in both capture and playback match perfectly. This can be approximated pretty closely in a studio, but not necessarily so when a disc is shipped to you and you play it at home without connection to the same timing signal.

3. Sampling theory assumes that the Analog to Digital (ADC) and Digital to Analog (DAC) are perfect. The former is able to translate an analog voltage to its exact digital counterpart and the other does the reverse. That is not true in real life no matter how close we can come to perfection. Taking 1.4 volt signal and dividing it by 64,536 makes for very small increments.

4. Sampling theory requires that the source signal and output (reconstructed) voltage are perfectly filtered to match the sampling rate requirements. In real life, perfect filters are hard to come by.

So as you see, there are areas to attack . But the math is not it....

I should have read this before my last post. Yes, the paper is like saying "energy is conserved exactly" and then sending someone out to measure where all the energy goes in your car.

 

[Gregadd]

This is a primer for me. I was taught the only dumb question is the one you never ask. So the second paper discusses higher sampler rates. Predictably he thinks that 88 or 96 is overkill and thinks 192 might even cause problems. If this is digital 101 for anybody feel free to ignore it. Or feel free to help me.

 

[amirm]

Amir,

So bit depth determines the total number and the size of voltage increments while sampling determines the bandwidth right?

At a very simplistic level yes. I don't want to confuse you right this minute to explain why in reality, it doesn't quite work that way . For now, a teaser with the explanation to come later. SACD uses a single bit for each sample. So that right there should tell you that this hole is a lot deeper than it seems .

Putting aside the deeper dive, you are correct.

If I got that right then it isn't just sampling but both to make digital better. There's something I don't get though. So here's my question. We know that the higher the bit rate the higher the dynamic range. Do the increments stay the same or more precisely, do the increments up to 96dB remain the same or do they get smaller when the bit depth is increased?

The analog output of your audio system is fixed and does not change based on what sampling rate you play. So it is the increments as you put it that get smaller with increased bit depth. A 24-bit signal divides the same 1.4 volt output into 16 million segments instead of 65 thousand for 16-bit audio.

The increased dynamic range comes from the fact that the noise floor, in theory, is pushed down by the higher resolution samples. In the example of 24-bit vs 16-bits, the 24-bit samples have 256 times lower noise (8 bits worth). Since the dynamic range is the ratio of the loudest to the faintest sound, it is proportionally increased by the the lowest values becoming smaller.

As a simple example, assume the lowest level is 1 and highest 10. The dynamic range would be 10. Now if I make the lowest level 0.1 because I can represent values 10X smaller, the dynamic range becomes 100.

Of course, you can invert this situation by turning the volume control higher for the higher resolution sample so that they both have equal noise floor. In that case, your system will get that much louder.

I noted that the above was in theory. In practice, we don't know how to get the noise to become lower than about 20 bits. As we go higher, we are simply reproducing noise, not the original signal (in both ADC and DAC). This is another advanced topic but the noise can be functional in improving audio quality but it doesn't do so because of increased resolution! I said this was an advanced topic .

Thanks in advance!

Jack

My pleasure. Thanks for asking good questions. Let's use this thread to advance our understanding of digital audio.

 

[amirm]

I don't think 44 kHz/16 bit is enough and also, there is the issue filtering, quantization and jitter which he doesn't address.

It is true. Just using the pro data rate of 48Khz would have given us nearly perfect scenario. If we are going to change it, then anything north of 50 to 55 Khz will do the job. Building good digital systems would have been cheaper and easier if they had just given us a bit more headroom.

As an aside, people keep talking about 96 KHZ/192 Khz as the better data rates but in reality, 88.4 Khz and 176.4 Khz are more optimal. Anyone know why?

 

[amirm]

This is a primer for me. I was taught the only dumb question is the one you never ask. So the second paper discusses higher sampler rates. Predictably he thinks that 88 or 96 is overkill and thinks 192 might even cause problems. If this is digital 101 for anybody feel free to ignore it. Or feel free to help me.

You mean why 96+ is overkill? If so, that is another advanced topic which takes some time to explain. I plan to do so in the future .

 

[Gregadd]

You mean why 96+ is overkill? If so, that is another advanced topic which takes some time to explain. I plan to do so in the future .

Good because this is not light reading.

Do you need more dots for better accuracy?
http://www.lavryengineering.com/docu...ing_Theory.pdf

 

[amirm]

Definitely not light reading. I stopped glancing it when I got the section in the middle where he says even he couldn't understand how the Sinc function did what it did and was trying to work it out through the course of the paper!