[xabu]

Quote:

^ Precisely.
 
xabu, here are some files I created to play around with: (all 16 bit, 44.1 kHz)
http://www.mediafire.com/?hy4n6e9cg1jt7s0 - 100, 1k and 10 kHz sine at below -80 dB
http://www.mediafire.com/?zq8t1ovnx7dn4q1 - the same, but below -100 dB
 
As mentioned before, dithering (1 of the 16 bits) was used to keep the noise floor down. And there are a lot of options to shape that noise to make it less audible than white noise.
 
Also (try to) listen to those files. 

I don't know what you did expect ... there is a tone audible for sure in both files.
 
What was it you wanted to state?
That 16 bit is enough to store this low tones?
... sure it's enough to store "some" value ...
 
Example:
If youd had only 9 possible values at hand to store something in a range from 0 - 60 (just some mathematical example, whatever these values represent doesen't matter they are just integers) and let's say these 9 possible values were 0, 8, 15, 23, 31, 49, 46, 54, 60. If you needed to store the value 44 it would be stored as 46.
 
 

 

[xnor]

Quote:

I don't know what you did expect ... there is a tone audible for sure in both files.
 
What was it you wanted to state?
That 16 bit is enough to store this low tones?
... sure it's enough to store "some" value ...
 
Example:
If youd had only 9 possible values at hand to store something in a range from 0 - 60 (just some mathematical example, whatever these values represent doesen't matter they are just integers) and let's say these 9 possible values were 0, 8, 15, 23, 31, 49, 46, 54, 60. If you needed to store the value 44 it would be stored as 46.

The purpose was to show that it doesn't work the way you described it in your example... (you would have noticed if you'd actually taken a closer look at the files)
and it's not just "some" value t_t 
 
And your last example shows this misunderstanding again. It doesn't matter if single samples don't exactly 'hit' the exact value. 
Digital audio is a bit more complicated..

 

[xabu]

Quote:

Quote:

I don't know what you did expect ... there is a tone audible for sure in both files.
 
What was it you wanted to state?
That 16 bit is enough to store this low tones?
... sure it's enough to store "some" value ...
 
Example:
If youd had only 9 possible values at hand to store something in a range from 0 - 60 (just some mathematical example, whatever these values represent doesen't matter they are just integers) and let's say these 9 possible values were 0, 8, 15, 23, 31, 49, 46, 54, 60. If you needed to store the value 44 it would be stored as 46.

The purpose was to show that it doesn't work the way you described it in your example... (you would have noticed if you'd actually taken a closer look at the files)
and it's not just "some" value t_t 
 
And your last example shows this misunderstanding again. It doesn't matter if single samples don't exactly 'hit' the exact value. 
Digital audio is a bit more complicated..

Well, now we get to the point
 
You wrote about the analog result of reproduction form the digital domain.
Obviously this is continuous, no doubt about that ... would be a bad D A C if not ...
But I wrote about the digital domain only so far and digital resolution, the A D C.
 
Regarding the analog reproduction I'm still not convinced that more digital resolution does not result in better reproduction ... among other things because of the fact that it is not possible to implement the nyquist theorem perfectly in practice.
 

 

[xnor]

Quote:

Regarding the analog reproduction I'm still not convinced that more digital resolution does not result in better reproduction ... among other things because of the fact that it is not possible to implement the nyquist theorem perfectly in practice.

 
That's good enough and it doesn't have to because nothing is perfect in analogue electronics.  

 
Why not convince yourself? Take a 24-bit file with high dynamic range, reduce the sample size to 16 bits (with dithering) and compare the files.
 
Done that .. good luck.
 
Or regarding perfect, infinite filters: read a book about digital signal processing first, and then convert an IIR into a FIR filter, apply both and compare the results. 

 (my EQ makes use of this)

 

[xabu]

Quote:

Quote:

Regarding the analog reproduction I'm still not convinced that more digital resolution does not result in better reproduction ... among other things because of the fact that it is not possible to implement the nyquist theorem perfectly in practice.

 
That's good enough and it doesn't have to because nothing is perfect in analogue electronics.  

 
Why not convince yourself? Take a 24-bit file with high dynamic range, reduce the sample size to 16 bits (with dithering) and compare the files.
 
Done that .. good luck.
 

 
Correct, making decisions about sound quality by actually listening to something is a really good point.  But I also want to comprehend it mathematically / technically ... with graphs etc.

 
As I said Im not yet convinced in one or the other way ... I still need more information about the whole subject matter ... I'm still learning

 
 

 

[xnor]

edited previous post a bit
 
Well, there's a lot of software (free) and also hardware out there to analyze and measure stuff. People have done that too. You'll just see tiny amounts of noise added, most probably completely inaudible in playback systems.
Compare this to lossless -> mp3 conversion. That adds tons of noise in comparison, clips, distorts the waveform and cuts off higher frequencies and still, it's transparent in many/most cases...

 

[D. Lundberg]

 
Quote:

Because you have only 1 bit you have more samples to "emulate" the missing bits (2.8224 MHz)  ... DSD and Sigma Delta DACs work completely differently from Ladder DACs and PCM.

You can't use more samples to emulate "missing" bits, and more importantly: there are no "missing" bits to emulate! More samples will just extend the bandwidth and more bits will just lower the noise floor.
DSD (which is based on Delta/Sigma) is actually a PCM-format and works the same way. The difference is that it needs noise shaping to be of any use, and that is what the extra bandwidth is used for.
The total dynamic range of a 1bit/2.8224MHz system is still 6dB, but lots of noise is moved upwards to lower the noise floor in the audible range.
 
Quote:

Regarding the analog reproduction I'm still not convinced that more digital resolution does not result in better reproduction ... among other things because of the fact that it is not possible to implement the nyquist theorem perfectly in practice.

Thankfully you don't need to perfectly implement the Nyquist theorem (at least not for use in audio). You just need to implement it well enough.
Here is an introduction to how the theorem works in practice:
http://www.lavryengineering.com/documents/Sampling_Theory.pdf

 

[xabu]

Quote:

Or regarding perfect, infinite filters: read a book about digital signal processing first, and then convert an IIR into a FIR filter, apply both and compare the results. 

 (my EQ makes use of this)

Well ...  to late today ... now I'd rather listen to some nice music

(... convert ...you mean by actually doing this ... programmatically ? what both ? compare what with what ?  EQ ?  we're derailing ... ... ah, I think it's too late in the evening ... )

 

[xabu]

Quote:

 
Quote:

Because you have only 1 bit you have more samples to "emulate" the missing bits (2.8224 MHz)  ... DSD and Sigma Delta DACs work completely differently from Ladder DACs and PCM.

You can't use more samples to emulate "missing" bits, and more importantly: there are no "missing" bits to emulate! More samples will just extend the bandwidth and more bits will just lower the noise floor.
DSD (which is based on Delta/Sigma) is actually a PCM-format and works the same way. The difference is that it needs noise shaping to be of any use, and that is what the extra bandwidth is used for.
The total dynamic range of a 1bit/2.8224MHz system is still 6dB, but lots of noise is moved upwards to lower the noise floor in the audible range.
 

 
Oooo.k. So the dynamic range of music stored on a SACD is only 6 dB  ... if you say so ...
 
Using "more samples to emulate missing" bits was a figure of speech ...
 
You're aware that 1 bit can hold only a quantity of 2 values? Can you actually explain how it is achieved that this 1 bit system nevertheless can handle/hold more than only 2 different values? It's achieved via the very fast switching of this 1 bit "switch".
 
That's my last post regarding this matter, because the title of this Thread is "24bit vs 16bit, the myth exploded!"

 

[xnor]

Yup, one/each bit = 6.02 dB of dynamic range, without applying techniques like noise shaping of course.
 
...but PCM != PDM, and that's the explanation right there 

 

[D. Lundberg]

Quote:

Originally Posted by xabu /img/forum/go_quote.gif
Oooo.k. So the dynamic range of music stored on a SACD is only 6 dB  ... if you say so ...

No, the total dynamic range of the system is ~6dB (0-1441kHz). The dynamic range in the audible range (20Hz-20kHz) is much larger (thanks to noise shaping).
 
Quote:

You're aware that 1 bit can hold only a quantity of 2 values? Can you actually explain how it is achieved that this 1 bit system nevertheless can handle/hold more than only 2 different values? It's achieved via the very fast switching of this 1 bit "switch".

Rounding to 2 steps means you'll get tons of quantization errors and those errors will represent white noise (if the signal is properly dithered). So less steps means more noise and thus higher noise floor.
I know it is hard to grasp that 2 steps can represent all the compexities of a waveform, but they very effectively can! Even if the sample rate is 44.1kHz the waveform will still be accurately represented in a 1 bit system (but the dynamic range will be very limited).

 

[xabu]

Quote:

Originally Posted by xnor /img/forum/go_quote.gif
 
...but PCM != PDM, and that's the explanation right there 

Exactly! And I'm glad we have some consent on that ... (... well, I pondered putting a

behind each of the following links ...

...)
 
 
And here's some more explanation of the rest ... but I still need some time to fully get the correlation between this 6 dB per bit stuff regarding voltage and accoustics.
You have to scroll down a bit

to get more text on the following sites ...
 
http://www.experiencefestival.com/a/Decibel_-_Reckoning/id/4843526
http://www.experiencefestival.com/a/Decibel_-_Uses/id/4843524
http://www.experiencefestival.com/a/Decibel_-_Typical_abbreviations/id/4843525
http://www.experiencefestival.com/a/Decibel_-_Definition/id/4843522

 

[Vitor Machado]

There is one thing I don't understand though:
 
Wouldn't it make more sense to use the extra bits not for increased dynamic range, but for more gradual steps in the quantization?
 
Suppose we have 3 bits (possible values: 000, 001, ... 111), and they represent, in order, -30, -20, -10, 0, 10, 20, 30, 40.
If we add one more bit, instead of going like -70, -60, ... , 70, 80 (which seems to be the analogous case for 16 vs. 24 bits if I understand correctly), why not -30, -25, -20, ... , 30, 35, 40, adding more steps instead of bigger range?
 
If someone could clarify things with some practical example like this it would be great!

 
EDIT: Better numbers for my example.

 

[xnor]

Quote:

If someone could clarify things with some practical example like this it would be great!

First post in this thread, followed by probably another hundred attempts of explanations to those who do not want or care to read a book about digital audio / signal processing, attend a course or at least read the Wikipedia articles that cover the basic fundamentals.
 
To repeat myself, the topic's a bit more complex than just dividing some numbers.

 

[Vitor Machado]

Quote:

First post in this thread, followed by probably another hundred attempts of explanations to those who do not want or care to read a book about digital audio / signal processing, attend a course or at least read the Wikipedia articles that cover the basic fundamentals.
 
To repeat myself, the topic's a bit more complex than just dividing some numbers.

1 - I did read the first post, and the first page. Did not read the whole thread because it's huge.
2 - I'm not going to read a book about digital audio / signal processing because I am busy with college, and have no such time available to delve deeply into the matter.
3 - I've read the Wikipedia articles and they did not cover my question with necessary detail.
 
I did find this example by xabu, a couple of pages ago:
 
"So lets say
 
with 1 bit we would resolve 6 dB into 2 values (e.g. 0 dB and 6 dB, nothing in between)
with 2 bit we would resolve 12 dB into 4 values (e.g. 0,4,8,12 dB, nothing in between)"
 
But that's strange, because people usually say to use 24-bits playback even if your source is 16-bits, because the source will be padded to 24-bits, and you get more range to waste with the digital volume control. But in this example, you just can't pad the 1-bit source to 2-bit at all (not without rounding 6 to 4 or to 8). So is everyone wrong in using 24-bit playback then (for 16-bit sources)?