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What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 01:40
by NOYB
The dynamic range of redbook audio CD (16-bit 44.1 KHz) is commonly cited as 90db, 96db, and 98db. And frequently cited as the S/N also. Which is correct? Please note, talking about the actual dynamic range and SQNR of the samples stored on the CD/in file. Not the perceived auditory dynamic range that can be created with dither sound shaping etc.

To begin with, as I understand, the samples are 16-bit signed. Not 16-bit unsinged. This being the case, only 15 bits actually represent the zero to peak amplitude. 15 * 6.02 db = 90.3db.

The formula 20Log10(min/max) says its 90db; 20Log10(1/32767) = -90.3db
(http://www.fte.com/WebHelpII/AES/Conten ... cRange.htm)

But that formula seems more like S/N ratio or SQNR (20Log10(2^Quantization-bits)): 20Log10(2^15) = 90.3db

In the signed 16 bit table below I come up with 84db dynamic range based on the difference between the smallest and largest. Think this would also yield a 90db SQNR.

Signed 16-bit:
s111 1111 1111 1111 -0 db (+/- 32767)
s011 1111 1111 1111 -6 db
s001 1111 1111 1111 -12 db
s000 1111 1111 1111 -18 db
s000 0111 1111 1111 -24 db
s000 0011 1111 1111 -30 db
s000 0001 1111 1111 -36 db
s000 0000 1111 1111 -42 db
s000 0000 0111 1111 -48 db
s000 0000 0011 1111 -54 db
s000 0000 0001 1111 -60 db
s000 0000 0000 1111 -66 db
s000 0000 0000 0111 -72 db
s000 0000 0000 0011 -78 db
s000 0000 0000 0001 -84 db (+/- 1)
0000 0000 0000 0000 -infinity db

s = sign bit
2.02 rounded to 2 as being 6db to reduce decimal clutter.

This is likely to open a can of worms and I'm sure it will be picked apart. I guess that's okay as long as we keep it civil and informative.

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 02:08
by Roberto C2H3
From what I have read out there, and more importantly, what I have been able to observe by trial and error, the CD has a superior potential dynamic range than vinyl.

I realize this does not answer your question at all. However, my answer does suggest that more important than the technical boundaries of a particular media is how it is used.

Case in point: I have a recently issued Pat Metheny CD purchased here in Buenos Aires that is mastered so loud as to be a real nuisance to listen to, even at low volumes. The distortion is atrocious, and the dynamic range has been devastated. I use it as a coaster.

Best from the Pampas,
roberto

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 02:28
by GuidoK
The way I see it s000 0000 0000 0000 is -90dB and the dithernoise is added to this level to mask the quantize errors.
So s000 0000 0000 0001 is +6dB and s111 1111 1111 1111 is therefore (+)90dB

Never realized dhe signed data would take away 6dB.
I always thought the dynamic range was 96dB

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 02:45
by pivot
Un-dithered CD (16/44.1k PCM) has, theoretically, a maximum 96 dB of dynamic range.

Dithering increases the range to 115 dB.

Depending upon whom you read LP has a dynamic range of circa 70-80 db.

Google "dithering", "dymanic range" and associate it to "CD" and "LP". GIYF

Maximum dynamic range in any medium is only realized by careful mastering and engineering. If the mastering compresses the original recording the "theoretical" dynamic range is all for crap.

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 03:29
by NOYB
pivot wrote:
08 Nov 2019 02:45
Un-dithered CD (16/44.1k PCM) has, theoretically, a maximum 96 dB of dynamic range.
Based on what? Not just what is claimed/cited by xyz but the work that arrives at that value.

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 08:31
by Erin1
pivot wrote:
08 Nov 2019 02:45
Un-dithered CD (16/44.1k PCM) has, theoretically, a maximum 96 dB of dynamic range.

Dithering increases the range to 115 dB.

Depending upon whom you read LP has a dynamic range of circa 70-80 db.

Google "dithering", "dymanic range" and associate it to "CD" and "LP". GIYF

Maximum dynamic range in any medium is only realized by careful mastering and engineering. If the mastering compresses the original recording the "theoretical" dynamic range is all for crap.
This is the correct answer!

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 08:36
by Erin1
NOYB wrote:
08 Nov 2019 03:29

Based on what? Not just what is claimed/cited by xyz but the work that arrives at that value.
Easy!
Each bit gives 6dB of dynamic range
6 X 16 = 96

https://www.google.com/amp/s/hbfs.wordp ... sited/amp/


https://www.google.com/url?sa=t&source= ... 48BfCx58Ee

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 08:45
by Erin1
NOYB wrote:
08 Nov 2019 01:40

20Log10(2^15) = 90.3db
The problem with your calculation is that CD is 16 bit, not 15 bit.

Each bit matters. You can not ignore the zero.

So the equation is

20Log10(2^16) = 96db

To correct your table:

0000 0000 0000 0000 -96 dB

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 10:30
by NOYB
Erin1 wrote:
08 Nov 2019 08:45
NOYB wrote:
08 Nov 2019 01:40

20Log10(2^15) = 90.3db
The problem with your calculation is that CD is 16 bit, not 15 bit.

Each bit matters. You can not ignore the zero.

So the equation is

20Log10(2^16) = 96db

To correct your table:

0000 0000 0000 0000 -96 dB
CD is not 16 bit. It is signed 16 bit two's compliment.

"0000 0000 0000 0000 -96 dB" ??? Are you saying the 0 value produces a non-zero signal level? If so then what produces a zero signal level?

I agree with the SNQR being 96.33 db. Based on...
The noise level is half the LSB (0.5; quantization error). So 20Log10(min/max) or 20Log10(2^Q-bits) = 96.33 db.

The dynamic range though I'm not sold on. Being that dynamic range is the difference between the smallest and the largest amplitude. Which in the positive is 1 to 32767 and in the negative is -1 to -32768.

To change the magnitude of a +/- alternating value by 6db both the positive and negative must be changed (increased or decreased) by a factor of 2 (or one of them must be changed by more than a factor of 2 while the other is changed by less than a factor of 2).

To symmetrically reduce -0db to -6db the positive 32767 has to be reduced by half and also the negative -32768 has to be reduced by half. Continuing this halving until only one bit remains set (the smallest signal that can be represented) results in -84db. A dynamic range of 84db.

Thus the smallest +/- alternating value that can be represented with signed 16 bits is -84db (LSB bit set and sign bit (MSB) alternating).

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 13:34
by NOYB
Maybe this table would be more correct. Gives 90 db dynamic range.

Code: Select all

Signed 16-bit          Two's Compliment     db   Value
0111 1111 1111 1111    0111 1111 1111 1111  -0 (+32767)
0100 0000 0000 0000    0100 0000 0000 0000  -6 (+16384)
0010 0000 0000 0000    0010 0000 0000 0000 -12 (+8192)
0001 0000 0000 0000    0001 0000 0000 0000 -18 (+4096)
0000 1000 0000 0000    0000 1000 0000 0000 -24 (+2048)
0000 0100 0000 0000    0000 0100 0000 0000 -30 (+1024)
0000 0010 0000 0000    0000 0010 0000 0000 -36 (+512)
0000 0001 0000 0000    0000 0001 0000 0000 -42 (+256)
0000 0000 1000 0000    0000 0000 1000 0000 -48 (+128)
0000 0000 0100 0000    0000 0000 0100 0000 -54 (+64)
0000 0000 0010 0000    0000 0000 0010 0000 -60 (+32)
0000 0000 0001 0000    0000 0000 0001 0000 -66 (+16
0000 0000 0000 1000    0000 0000 0000 1000 -72 (+8)
0000 0000 0000 0100    0000 0000 0000 0100 -78 (+4)
0000 0000 0000 0010    0000 0000 0000 0010 -84 (+2)
0000 0000 0000 0001    0000 0000 0000 0001 -90 (+1)

0000 0000 0000 0000    0000 0000 0000 0000 -infinity (0)

1000 0000 0000 0001    1111 1111 1111 1111 -90 (-1)
1000 0000 0000 0010    1111 1111 1111 1110 -84 (-2)
1000 0000 0000 0100    1111 1111 1111 1100 -78 (-4)
1000 0000 0000 1000    1111 1111 1111 1000 -72 (-8)
1000 0000 0001 0000    1111 1111 1111 0000 -66 (-16
1000 0000 0010 0000    1111 1111 1110 0000 -60 (-32)
1000 0000 0100 0000    1111 1111 1100 0000 -54 (-64)
1000 0000 1000 0000    1111 1111 1000 0000 -48 (-128)
1000 0001 0000 0000    1111 1111 0000 0000 -42 (-256)
1000 0010 0000 0000    1111 1110 0000 0000 -36 (-512)
1000 0100 0000 0000    1111 1100 0000 0000 -30 (-1024)
1000 1000 0000 0000    1111 1000 0000 0000 -24 (-2048)
1001 0000 0000 0000    1111 0000 0000 0000 -18 (-4096)
1010 0000 0000 0000    1110 0000 0000 0000 -12 (-8192)
1100 0000 0000 0000    1100 0000 0000 0000  -6 (-16384)
1000 0000 0000 0000    1000 0000 0000 0000  -0 (-32768)

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 14:58
by NOYB
This is what I've come to think is correct:

SQNR* = 20Log10(2^Q-bits) = 20Log10(2^16) = 96.33 db

Dynamic Range = 20Log10(min/max) = 20Log10(1/32767) = 90.31 db

* Signal Quantization Noise Ratio

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 15:02
by Vinylfreak86
Japanese are upgrading standard CD`s into a better format, so there is still a lot of space to make a compact disc better. But you cannot upgrade LP into a better format, because it is simply mechanical. These 180g versions of the last decade are just commercial bluff and unpractical to handle.

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 08 Nov 2019 18:35
by pivot
Red book Compact Disc is 16 bit word length 44.1 kHz sampled Pulse Code Modulation. The Japanese or the Swiss or the suburbs of Paramus, New Jersey cannot make a "better" CD.

Change the coding and you no longer have a "Compact Disc" by definition. The maximum resolution, signal to noise ratio, and dynamic range are set. SACD and DVD-A are both "better" but they are not "Compact Disc". There may be a Compact Disc layer encoded on a SACD or DVD-A but the CD layer has the same limitations as a standard CD.

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 09 Nov 2019 01:06
by Roberto C2H3
Vinylfreak86 wrote:
08 Nov 2019 15:02
These 180g versions of the last decade are just commercial bluff and unpractical to handle.
Amen to that, brother... 8)

Re: What is the dynamic range and S/N ratio of CD format?

Posted: 09 Nov 2019 03:11
by Hanuman
If I'm not wrong there's a bit of a difference in measurement of S/N ratio in a digital versus analogue system. In a PCM system, as we know, there exists an easily seen absolute maximum recorded level that can't be exceeded no matter what. That level becomes the reference level against which the S/N ratio is calculated. It follows that the resulting number is also the dynamic range.

Anaogue tape recorders don't have such an obvious ceiling and S/N tends to be referred to a more arbitrary signal level, perhaps a specific level of magnetic flux or a particular level of distortion. The recorder may be capable of recorded levels that exceed that reference - analogue headroom - meaning that the actual working dynamic range might appear to be higher than the S/N ratio - I think - I've never been a professional audio engineer. My expertise is in broadcast video.