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

compact disc, dacs, mp3 players and streaming audio
GuidoK
member Posts: 216
Joined: 05 Dec 2007 21:20
Location: Rotterdam, Netherlands

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

In a world where quantize errors don't exist, in a world where there would be no dithering because of that, the SNR for 16 bit audio would be infinite (asymptote on a curve) according to analog's and TI/BB's definitions (and wikipedia and virtually all other sources), and so would the dynamic range.
According to TDY's definition its 90dB for 16 bit audio. They have a different definition.

But I think we live in a world where quantize errors do exist. and where digital signals are getting dithered.

NOYB
member  Posts: 249
Joined: 01 Jul 2019 01:12

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

The dynamic range of a data set is the ratio between the maximum and the minimum non zero representable values expressed as db.
Dither and quantize error to your hearts content. It has no effect on the ratio between the maximum and the minimum non zero representable values of the data set. They will remain 1 and 32767. And -1 and -32768.

And the data set dynamic range will remain db = 20Log(max/min).
20Log(32767/1) = 90.31 db
20Log(-32768/-1) = 90.31 db

GuidoK
member Posts: 216
Joined: 05 Dec 2007 21:20
Location: Rotterdam, Netherlands

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

yes, all true according to the definition from Teledyne.

But that is not a calculation of the SNR. (none of the max/min data you use is noise)
And Analog Devices (first manufacturer of any cmos DA converter) say in digital audio dynamic range is the same as SNR and give a different formula.

Same goes for TI/BB.
Give same formula.

Not my definition but theirs. I'm not the writer of the documents in the links I gave you.
I don't care what definition is used. Each definition calculates something different. The one calculates the difference between the lowest sine signal and highest sine signal, being the one from TDY, and the other one calculates the difference between the noise floor or quantize error level and highest sine signal, being the one from AD and TI/BB, and that one is also listed in wikipedia. Maybe they wrote that entry.

NOYB
member  Posts: 249
Joined: 01 Jul 2019 01:12

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

Based on 6.02db x 16 = 96db
Which is incorrect for signed 16-bit two's compliment linear PCM (redbook audio CD) dynamic range.

https://www.analog.com/en/education/edu ... range.html
Dynamic Range of a digital signal is defined as the ratio of the maximum full scale signal representation to the smallest signal the DSP or converter can represent. For an N-bit system, the ratio is theoretically equal to 6.02N.
The correct N for signed 16-bit two's compliment linear PCM (redbook audio CD) is 15.

Werner
long player  Posts: 1347
Joined: 31 May 2002 00:00
Location: Antwerpen

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

NOYB wrote:
18 Nov 2019 20:20
The correct N for signed 16-bit two's compliment linear PCM (redbook audio CD) is 15.
Nope. You are wrong. In calculating the theoretical SNR and dynamic range (which are equal in a linear system) the numerical representation does not play a role. The largest signal one can encode with an N-bit linear scheme is 2^N-1, the smallest is 1. The dynamic range is the ratio of both. Doesn't matter if it is straight or 2's complement. With CD you can swing between -32768 and 32767 on the high side, and 0 and 1 on the low side. The ratio remains 96dB.

Or try this approach: you can always take a CD data stream and re-encode it as straight, positive-only PCM. Does this change the informational content? Not at all.

--

Actual SNR is a little bit less than 96dB, because dither must be used during encoding. When talking PCM always assume dithering: undithered PCM should be a criminal offense.

Not wanting to brag, but, having founded and owned two successful semiconductor companies, companies that amongst others made ADCs and DACs, I think I know a bit or two about this. And no, I was not the CFO, nor the janitor.

NOYB
member  Posts: 249
Joined: 01 Jul 2019 01:12

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

Werner wrote:
21 Nov 2019 06:10
In calculating the theoretical ...
Nuff said.

Maximum amplitude (full scale):
positive phase peak value: +32767
negative phase trough value: -32768

Each phase is contained in a range of 32767. 0 to 32767 for the positive phase and -1 to -32768 for the negative phase.

For each -6db change, BOTH the positive phase AND the negative phase is reduced by one half (1/2). Symmetrically. Not just one phase or the other. Changing only one phase or the other inflicts substantial distortion.

When a full scale signal is reduced by 6db, it's positive phase peak value becomes 16384, and it's negative phase trough value becomes -16384.

There are 15 steps of -6db available from full scale for a dynamic range of 90dB.

-0dB: positive phase value: +32767 and negative phase value: -32768
-6dB: positive phase value: +16384 and negative phase value: -16384
-12dB: positive phase value: +8192 and negative phase value: -8192
-18dB: positive phase value: +4096 and negative phase value: -4096
-24dB: positive phase value: +2048 and negative phase value: -2048
-30dB: positive phase value: +1024 and negative phase value: -1024
-36dB: positive phase value: +512 and negative phase value: -512
-42dB: positive phase value: +256 and negative phase value: -256
-48dB: positive phase value: +128 and negative phase value: -128
-54dB: positive phase value: +64 and negative phase value: -64
-60dB: positive phase value: +32 and negative phase value: -32
-66dB: positive phase value: +16 and negative phase value: -16
-72dB: positive phase value: +8 and negative phase value: -8
-78dB: positive phase value: +4 and negative phase value: -4
-84dB: positive phase value: +2 and negative phase value: -2
-90dB: positive phase value: +1 and negative phase value: -1

-oodB: positive phase value: 0 and negative phase value: 0

oo represents infinity

Werner
long player  Posts: 1347
Joined: 31 May 2002 00:00
Location: Antwerpen

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

NOYB wrote:
03 Dec 2019 03:53
Werner wrote:
21 Nov 2019 06:10
In calculating the theoretical ...
Nuff said.
You may want to get yourself a textbook on signal theory. And read it.

And consider the 0 +1 0 or 0 -1 0 case.

Or consider the quantisation error, which is 1/2 LSB.

NOYB
member  Posts: 249
Joined: 01 Jul 2019 01:12

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

Werner wrote:
03 Dec 2019 06:28
NOYB wrote:
03 Dec 2019 03:53
Werner wrote:
21 Nov 2019 06:10
In calculating the theoretical ...
Nuff said.
You may want to get yourself a textbook on signal theory. And read it.

And consider the 0 +1 0 or 0 -1 0 case.

Or consider the quantisation error, which is 1/2 LSB.
So you can't refute the case presented. Instead post stuff without explaining how you think that it invalidates the case.

The consideration of "0 +1 0" and "0 -1 0" is why it is not in the case presented. Please show how you believe that it invalidates the case.

Werner
long player  Posts: 1347
Joined: 31 May 2002 00:00
Location: Antwerpen

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

Once more.

The definition of dynamic range is the ratio of the maximum undistorted encoded signal to the channel's noise floor. For a digital channel with quantisation step Q and no dither the noise floor equals the quantisation error, which is +/-Q/2 peak and 0.3Q RMS. These are the definitions. If you don't accept these then this discussion is pointless.