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

compact disc, dacs, mp3 players and streaming audio
Hanuman
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Re: What is the dynamic range and S/N ratio of CD format?

Post by Hanuman » 09 Nov 2019 15:47

NOYB wrote:
09 Nov 2019 09:02
The practical useful dynamic range decreases as frequency decreases due to the relationship between frequency and sampling rate.
How does that work?

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

Post by NOYB » 10 Nov 2019 03:20

Erin1 wrote:
09 Nov 2019 12:20
NOYB wrote:
09 Nov 2019 11:17

How does two's complement explain that I'm going wrong?
Well, everyone else in the world calculates 96dB signal to noise. That's what I was taught at electronics school. I passed the test too!

The link I provided you earlier explains it.

You're obviously going wrong somewhere.
Who in the world is not calculating 96 db signal to noise? Certainly not me. I said much earlier in this thread that the SQNR is 96 db.

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

Post by NOYB » 10 Nov 2019 03:23

Hanuman wrote:
09 Nov 2019 15:47
NOYB wrote:
09 Nov 2019 09:02
The practical useful dynamic range decreases as frequency decreases due to the relationship between frequency and sampling rate.
How does that work?
Missspoke there. It has nothing to do with finished product CD. Has to do with recording, mixing and editing. For instance increasing the volume of a very weak signal.

A 40 Hz signal covers the span of 1102 samples (44100/400 = 1102.5). If the signal level is low enough, say -50 db, the amplitude of the low frequency wave form does not rise and fall fast enough to prevent large blocks of consecutive identical samples due to the quantization granularity. If the frequency and signal level are low enough it can end up being more like a square wave.

But of course studios etc. don't work in the 44.1 KHz 16-bit realm. Though given the right combination of signal level, frequency and sampling rate it could be experienced even with 192 KHz 24-bit.

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

Post by Hanuman » 10 Nov 2019 03:31

NOYB wrote:
10 Nov 2019 03:23
If the signal level is low enough, say -50 db, the amplitude of the low frequency wave form does not rise and fall fast enough to prevent large blocks of consecutive identical samples due to the quantization granularity.
Yes, that's loss of resolution, confirmed by a composer/engineer friend of mine as a real thing back in the day, with emphasis on "the day" since 16-bit production started to disappear in the nineties. I don't think it's dependent on frequency BTW.
Last edited by Hanuman on 10 Nov 2019 03:50, edited 1 time in total.

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

Post by GuidoK » 10 Nov 2019 03:37

Erin1 wrote:
09 Nov 2019 12:20
Well, everyone else in the world calculates 96dB signal to noise. That's what I was taught at electronics school. I passed the test too!
This is a double fallacy (argumentum ad verecundiam and argumentum ad populum)

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

Post by NOYB » 10 Nov 2019 04:51

Hanuman wrote:
10 Nov 2019 03:31
NOYB wrote:
10 Nov 2019 03:23
If the signal level is low enough, say -50 db, the amplitude of the low frequency wave form does not rise and fall fast enough to prevent large blocks of consecutive identical samples due to the quantization granularity.
Yes, that's loss of resolution, confirmed by a composer/engineer friend of mine as a real thing back in the day, with emphasis on "the day" since 16-bit production started to disappear in the nineties. I don't think it's dependent on frequency BTW.
I believe it occurs at all frequencies below the Nyquist frequency and is exacerbated as the signal frequency goes lower due to the increasing amount of quantization errors per cycle as frequency decreases.

Though this isn't really pertinent to the subject of this thread and thus it was a mistake on my part to injected it.

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

Post by NOYB » 13 Nov 2019 02:33

Erin1 wrote:
08 Nov 2019 08:36
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
Each quantization bit gives 6db of dynamic range. But there are only 15 quantization bits. Not 16. The 16th bit (MSB) provides only that the quantization is positive or negative. Not magnitude.

It seems to me that we probably agree on the SQNR being 96.33 db. Though we may not be in agreement on the formula and the dynamic range.

Seems like your SQNR formula would be...
20Log(2^16) = 20Log(65536) = 96.33 db SQNR

Which even though it arrives at the correct value, would be an incorrect formula because the quantization noise level should be half the LSB value. Thus if truly 16 bits the formula should be...
20Log(2^16/0.5) = 20Log(131072) = 102.35 db SQNR

Were as the correct formula I believe would be...
20Log(2^15/0.5) = 20Log(65536) = 96.33 db SQNR


With the LSB being the smallest value possible (1) and the quantization noise being one half the LSB (0.5), the dynamic range is then 6db less than the SQNR db.
20Log(2^15/1) = 20Log(32768) = 90.31 db dynamic range.

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

Post by jdjohn » 13 Nov 2019 23:13

Seems all of the discussion above is theoretical anyway.

"Digital audio at 16-bit resolution has a theoretical dynamic range of 96 dB, but the actual dynamic range is usually lower because of overhead from filters that are built into most audio systems." ... "Audio CDs achieve about a 90-dB signal-to-noise ratio." https://books.google.com/books?id=w0vsd ... &q&f=false

What's interesting is that DSD/SACD only has 1 bit, but sampling of 2.8MHz, and provides (in theory) almost 120db of dynamic range - roughly equivalent to (theorectical) 20bit PCM audio.

P.S. I'm not going to argue about any of the above, but merely found the information while doing a little research on my own. Feel free to pick it apart as I have no vested interest in it.

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

Post by NOYB » 14 Nov 2019 05:06

jdjohn wrote:
13 Nov 2019 23:13
Feel free to pick it apart as I have no vested interest in it.
Okay I'll pick little since you granted permission. ;)
jdjohn wrote:
13 Nov 2019 23:13
Seems all of the discussion above is theoretical anyway.
The digital data contained on a redbook audio CD has exact non theoretical values and thus an exact actual, not theoretical, dynamic range.
jdjohn wrote:
13 Nov 2019 23:13
"Digital audio at 16-bit resolution has a theoretical dynamic range of 96 dB, but the actual dynamic range is usually lower because of overhead from filters that are built into most audio systems." ... "Audio CDs achieve about a 90-dB signal-to-noise ratio." https://books.google.com/books?id=w0vsd ... &q&f=false
Completely disregards the fact that redbook audio CD data is signed and therefore there are only 15 bits representing magnitude. Thus the redbook audio CD data has a dynamic range of 20Log(max/min) = 20Log(2^15/1) = 90.33 db.
jdjohn wrote:
13 Nov 2019 23:13
What's interesting is that DSD/SACD only has 1 bit, but sampling of 2.8MHz, and provides (in theory) almost 120db of dynamic range - roughly equivalent to (theorectical) 20bit PCM audio.
The opening paragraph of this thread is clear that it is about "redbook audio CD (16-bit 44.1 KHz)". But nevertheless DSD/SACD is still bits. Just more of them in a different format. Regardless of which format, generally the more bits, the more accurate the representation.

But this thread is about redbook audio data SQNR and dynamic range. So far it seems we agree on the SQNR = 96.33 db. But not the dynamic range.

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

That is 15 steps of 6db. 6db x 15 steps = 90db dynamic range.