[RRod]

  I think what he says is in part my fault because I insisted on the fact that the track didn't need to have hires content for the DAC to end up with high sample rate.

 
Is ok, am chillin' 

 

[BackToAnalogue]

Me too, but more Maths tomorrow I'm afraid.

 

[BackToAnalogue]

 harmonic distortions are indeed done from 1sine at a time. and they keep only whatever is present at the multiples of the input frequency(harmonic). 
THD+noise is the same but they keep everything except the original sine.
and only IMD is done with 2freqs at once.
for how it's done on vinyl the first link I posted before explains it (they obviously use a test record, but it's pretty much the same idea).

 


"As I suspected Watson"

 

[esldude]

Don't worry I haven't given up yet. You say

"Higher sampling rates don't introduce higher frequencies, they allow us to capture them without aliasing, which is the whole point of the ADCs anti-aliasing filter. "

Firstly I did not say that higher sample rates introduce higher frequencies, though you implied it in your previous post.

I said the same thing as you i.e. they allow us to capture higher frequencies. Which you seem to think we actually do but in fact we don't. Why would we capture something that we can't hear? Band limiting stops anything above 20KHz getting through because it is a waste of space.

If you don't capture high frequencies then you can't reconstruct such a good square wave. Fine, interesting, if you add more samples (not frequencies) it improves the interpolation i.e. the shape of the square wave. Also fine, interesting. So a wider frequency range or more samples both improve the shape of the square wave. But not in quite the same way. So it shows us something about our equipment and is a good illustration of how interpolation works. But this is Mathematics. And, it doesn't tell us much, if anything, about how good the audio signal a DAC tested this way will produce. Though I am sure there are particular artifacts that Engineers look for using a square wave test.

You are still confusing sample rate with frequencies captured. When you say -

"As you can see the difference, in terms of RMS, between the the ideal square and the band- limited squares goes to zero as we add in more frequencies."

The difference is due to more samples NOT more frequencies. All three have exactly the same band limits, 20Hz to 20KHz or thereabouts.

I want to come back to the harmonic distortion post, can someone confirm for me if I am correct that this is measured using a pure SIN wave which is somehow compared after passing through the equipment to see how much it has been changed i.e. distorted ?

Some readers may think that I am deliberately not replying to or ignoring the posts pointing out all the problems with vinyl. They would be correct in that assumption, and that is because I agree with most if not all of them.

Look if you have 44.1 khz sample rates you can record frequencies to near 22,050 hz.  They brickwall filter between 20khz and 22.05 khz to prevent aliasing.
 
If you use 192 khz sample rates you can record frequencies up near 96 khz.  Normally the 80 khz to 96 khz band will be brickwall filtered to prevent aliasing.  And though humans can't hear 80 khz, hirez recordings potentially have that response.  They don't stop at 20 khz.   And that is all you get from higher sample rates is extended frequency response.  You don't get better drawn waves at lower frequencies from interpolation.  You get one thing from higher rates and that is more bandwidth.
 
The reason the extended response draws a better square wave is a squarewave is a sine wave and all of the odd harmonics.  More bandwidth allows you to draw in more harmonics.  The closer to infinite harmonics you get the more square it will become. 
 
http://xiph.org/video/vid2.shtml
 
This is a super good video about how digital really works.  24 minutes, and well worth watching.  Explains a ton of ideas in a simple easy to understand manner.  They use very high quality analog signal generators and analyzers to show what digital can do and how it works.  It is most informative. 

 

[germanium]

Look if you have 44.1 khz sample rates you can record frequencies to near 22,050 hz.  They brickwall filter between 20khz and 22.05 khz to prevent aliasing.

If you use 192 khz sample rates you can record frequencies up near 96 khz.  Normally the 80 khz to 96 khz band will be brickwall filtered to prevent aliasing.  And though humans can't hear 80 khz, hirez recordings potentially have that response.  They don't stop at 20 khz.   And that is all you get from higher sample rates is extended frequency response.  You don't get better drawn waves at lower frequencies from interpolation.  You get one thing from higher rates and that is more bandwidth.

The reason the extended response draws a better square wave is a squarewave is a sine wave and all of the odd harmonics.  More bandwidth allows you to draw in more harmonics.  The closer to infinite harmonics you get the more square it will become. 

http://xiph.org/video/vid2.shtml

This is a super good video about how digital really works.  24 minutes, and well worth watching.  Explains a ton of ideas in a simple easy to understand manner.  They use very high quality analog signal generators and analyzers to show what digital can do and how it works.  It is most informative. 

Excellent video.

What it doesn't explain though is why some digital DAC's still sound better than others to me. At this point I would like to introduce the concept of tranfer function. This is something that one person named Bob Carver figured out not only that this property existed but could measure it & alter it. This he did in the analog domain with power amps but the same principals apply to the final output of DAC's. My experimentation has lead my to believe that significant improvements can be made in the analog output section of the DAC without harming or significantly altering the specs of the DAC.

Note that when Bob Carver was doing his transfer function modification he was in fact significantly altering the specs of his amps to sound like a completely different type of amp originally of Anouther manufacturer which caused some problems for him down the road. I have seen though that one really don't have to alter specs of the DAC's to significantly alter the sound in significant & excellent ways.

Note that when I modify DAC's I'm not trying to copy some others sound but to be able to listen deeper into the recording with improved clarity across the whole frquency range. In other words be able to extact as much of the available resolution without altering frequency response or distortion in any significant way. Some of my ideas also work well in analog output of any analog device. While I do see digital as pretty much perfect for music reproduction I find the the analog output sections to still be wanting even in much of the very expensive gear even though specs are universally excellent even for many lower priced DAC's & amps to my ears. This has been true for me all the time that I have been in this hobby. Music whether digital or analog just lacked the life of what I hear with live music even just in passing by live music. I wanted to capture that type of sound as well, that is the sense of life that you typically only get with live music. Many high end systems sound nice but still lack that life that I want.

 

[BackToAnalogue]

I agree excellent video, I had already read his paper which I recommend to anyone trying to understand this subject and I think you will get more from the video if you read that first. I kept stopping it and repeating bits.

But he is incorrect about 24 bits not mattering. I found his explanation very plausible and I couldn't see any holes in it so I accepted it for quite a while and kept telling people that these guys were wasting space on bits when it would be better used on samples. The explanation of why he is wrong is not straightforward but it is to do with information and how information is carried in wave forms.

To understand this a bit, watch the video and the part where he shows the perfect output SIN wav, and then shows a spectrogram of the same waveform and you can see several spikes which are harmonics introduced by the DAC (aliasing I imagine?). So they are clear and obvious on the spectrogram. But on the SIN wave where are they? They must be in there because we know that it carries this information, we have just seen great big spikes of it, so where is it?

He is also wrong about higher sample rate not mattering and I thought that was pretty obviously wrong. Not his fault he is an electronics guy, almost certainly a very good one, but his Maths is a bit flaky.

 

[castleofargh]

I agree excellent video, I had already read his paper which I recommend to anyone trying to understand this subject and I think you will get more from the video if you read that first. I kept stopping it and repeating bits.

But he is incorrect about 24 bits not mattering. I found his explanation very plausible and I couldn't see any holes in it so I accepted it for quite a while and kept telling people that these guys were wasting space on bits when it would be better used on samples. The explanation of why he is wrong is not straightforward but it is to do with information and how information is carried in wave forms.

To understand this a bit, watch the video and the part where he shows the perfect output SIN wav, and then shows a spectrogram of the same waveform and you can see several spikes which are harmonics introduced by the DAC (aliasing I imagine?). So they are clear and obvious on the spectrogram. But on the SIN wave where are they? They must be in there because we know that it carries this information, we have just seen great big spikes of it, so where is it?

He is also wrong about extra samples not mattering and I thought that was pretty obviously wrong. Not his fault he is an electronics guy, almost certainly a very good one, but his Maths is a bit flaky.

hey long time no see ^_^.
more bits only add values that are lower than theoretical -96bit, so for the audio from 0 to let's say -80db, adding bits will not change the signal at all. all it can do is deal with noises that are below -80db, and the most obvious noise will be quantization noise from 16bit. so for music recorded most of the time between 0 and -60db, more bits don't do anything as the added bits can't be used to interpolate the signal, the added values are all used for quieter signal values. one simple way to know it works like that is the fact that 1more bit keeps adding about 6db of possible dynamic, showing very clearly that added bits only go below the existing signal.

 

[lauris3722]

Not music, but microphone. I had many anolog microphones, at different value (5$-50$), my most recent purchase was CAD-U37 microphone, which is an USB/Digital microphone.. The change was pretty big, there was absolutely no background noise and the sound was crystal clear with deep bass (very good for recording guitar, etc.). Also, I had no problems for recording volume. Every single anolog microphone had low recording volume, digital's one volume was 10x louder (I usually keep the recording volume at 30-50%). Never once I experienced such quality with anolog microphones, but it might aswell be the microphone itself, not the anolog vs digital..

 

[BackToAnalogue]

How on earth does a digital microphone work?

If it has a diaphram or any other mechanical device to capture the sound wave then it is analogue with an ADC in the microphone instead of the mixing desk. Or am I going completely bonkers here?

 

[esldude]

I agree excellent video, I had already read his paper which I recommend to anyone trying to understand this subject and I think you will get more from the video if you read that first. I kept stopping it and repeating bits.

But he is incorrect about 24 bits not mattering. I found his explanation very plausible and I couldn't see any holes in it so I accepted it for quite a while and kept telling people that these guys were wasting space on bits when it would be better used on samples. The explanation of why he is wrong is not straightforward but it is to do with information and how information is carried in wave forms.

To understand this a bit, watch the video and the part where he shows the perfect output SIN wav, and then shows a spectrogram of the same waveform and you can see several spikes which are harmonics introduced by the DAC (aliasing I imagine?). So they are clear and obvious on the spectrogram. But on the SIN wave where are they? They must be in there because we know that it carries this information, we have just seen great big spikes of it, so where is it?

He is also wrong about extra samples not mattering and I thought that was pretty obviously wrong. Not his fault he is an electronics guy, almost certainly a very good one, but his Maths is a bit flaky.

You did understand his perfect sine wave as initially shown was completely analog from start to finish?  And you did see the spectrum analyzer shows a few very low level peaks of harmonic distortion while everything was fully analog.  And then did you notice when he inserted an AD/DA conversion right in the middle the analog spectrum analyzer after the AD/DA conversion showed exactly the same peaks.  Those peaks on the sine wave were not aliasing when it was analog.  So neither were they when an identical spectrum was shown after putting AD/DA in the middle .  Those very low levels of harmonics would not be seen in an o-scope trace (you need maybe 3% for it to be visible that way).  They do show up in spectrum analysis.  And they did this both as purely analog and after going through a digital conversion in the middle. 
 
As for being wrong about extra samples not mattering, I am not sure if you are referring to 8 vs 16 bit or 16 vs 24 or if you are referring to sample rate differences.  He did indicate a good waveform is obtained at 8 or 16 bit.  The noise floor differs.  Same with 24 bit.  You get the waveform the noise floor is lowered.  You pretty much don't get noise in electronics low enough to use 24 bit, more like 20 bit is where it bottoms out right now.  16 bit is pretty good though yes a bit noisier than 24 bit.  So I fail to see the flaky math. 
 
He also is one of the people behind Ogg Vorbis encoding so not just an electronics guy.  Whatever kind of guy he is, within context there isn't much one can call wrong in the video.  What one could quibble about slightly are things that he stated as generally true and not really good subjects to delve into during such a simple video presentation.

 

[BackToAnalogue]

I am determined to try and make this reply short.

Guys please go back and think about the question I posed.

Where is that information about harmonics? There is quite a lot of information, you have seen it in big spikes. Where is it?

You all know the answer to that question. So when you get it, think about what it tells you about the data relating to those harmonics and how that data is carried in the SIN wave. If you go through that exercise yourself and think about it without keep saying to yourself, this is obvious, he hasn't understood it properly, then I am pretty sure that at least one of you will realise for yourselves what I am on about. And if you do that you will understand it far better than if I keep trying to explain it in Mathematics or logic or example or whatever.

Quick replies
castle- yes that is where I was until a few weeks ago. I understand all that, it isn't wrong just incomplete.
elsdude.- No I made a slight mistake I should have watched the video again first. I did say 'Aliasing I imagine?' which means' I am too lazy too check because it doesn't matter for this particular point', thank you for correcting me. So the harmonics were in the original analogue wave not due to aliasing or harmonic distortion (I had just been reading about Harmonic Distortion so probably confused myself) and it shows that the ADC/DAC combination has sufficient precision to be able to record them and then reproduce them accurately. As I said this video really helps understand this stuff particularly if you keep asking yourself questions as you watch it. But please go back to the point I am trying to illustrate. I started to understand how and why he was wrong about bit depth a few weeks ago but it was thinking about this a couple of nights ago that really solidified my understanding.

Also sorry I didn't mean 'just an Electronics guy' as in not smart etc. I am not an Electronics guy or a Hardware guy and I am always impressed by people who are good at that stuff. It is very complicated and requires a lot of knowledge and care and attention to detail. I am just trying to highlight that people from different disciplines look at the same thing differently. That is how you test ideas and find things out.

I do try to be very precise about language and terms and welcome any corrections on that score.

If I say sampling rate, I mean sampling rate, not frequency response, not number of terms in the interpolation, not bit depth. I do sometimes make mistakes and switch two terms by accident and if I do that please point it out and I will correct. But I try very hard not to. I read everything two or three times before I hit send (if it is technical, not if I am being light hearted). And then I come back and reread it a few hours later and quite often spot some lazy or imprecise or incorrect term and I correct it.

So to me it is pretty obvious why more samples means better accuracy, but it wasn't obvious at all why 24 bits is a lot better than 16, even if in reality it was only 20 or 21. In fact I was totally convinced by his argument just like you are.

The statement that 'more samples means greater accuracy' is a gross oversimplification and I will return to it another time soon. Just leave that for now.

 

[BackToAnalogue]

Having spent a couple of hours reading about Monty I do realise that saying 'his Maths is just a bit flaky' is, to say the least, rather impertinent of me. So Monty, should you ever read this, no offence intended, I am not one of those trolls, I have given this a great deal of thought. You are a smart guy with integrity and you will love this when you get it.

Monty's video and more importantly, his write up, is the only complete explanation I was able to find which brings it all together and explains so many of the misconceptions. But I did spot two important holes and have spent a lot of time thinking about them. And I have now understood why one of them is very important indeed.

I am not going to go back and edit it out BTW.