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

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

Post by NOYB » 09 Nov 2019 09:02

Hanuman wrote:
09 Nov 2019 03:11
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.
The noise level is half the LSB value (0.5). So SQNR = 20Log(32767/0.5) = 96.33 db. The CD cannot contain a value smaller than 1 nor larger than 32767. So DR = 20Log(32767/1) = 90.31 db.

However please note that the practical useful dynamic range has a frequency dependency also. The practical useful dynamic range decreases as frequency decreases due to the relationship between frequency and sampling rate.

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

Post by Erin1 » 09 Nov 2019 10:12

NOYB wrote:
08 Nov 2019 10:30


CD is not 16 bit. It is signed 16 bit two's compliment.
You are concocting a story to fit in with your mistaken beliefs.

Please do more research from reputable sources. That's the most polite way I can say this.

Myself and other people are trying to help you but you're not listening.

In an earlier post I linked two reputable sources. One showed the working out of the complex maths for the 6dB dynamic range per bit - which you asked for.
The other link was to Analog Devices who actually make DAC chips.

Did you read?
Do you want to learn?

Or do you still think everyone else is wrong?

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

Post by Erin1 » 09 Nov 2019 10:24

Here is a measurement of an old DAC chip -AD1865. Signal to noise ratio of approximately 120dB (with oversampling)
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NOYB
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Re: What is the dynamic range and S/N ratio of CD format?

Post by NOYB » 09 Nov 2019 10:26

Erin1 wrote:
09 Nov 2019 10:12
NOYB wrote:
08 Nov 2019 10:30


CD is not 16 bit. It is signed 16 bit two's compliment.
You are concocting a story to fit in with your mistaken beliefs.
Are you saying it is not signed 16 bit two's compliment?

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

Post by NOYB » 09 Nov 2019 10:29

Erin1 wrote:
09 Nov 2019 10:24
Here is a measurement of an old DAC chip -AD1865. Signal to noise ratio of approximately 120dB (with oversampling)
Please go back and read the first paragraph in the opening post of this thread.

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

Post by Erin1 » 09 Nov 2019 10:38

NOYB wrote:
09 Nov 2019 10:26
Erin1 wrote:
09 Nov 2019 10:12
NOYB wrote:
08 Nov 2019 10:30


CD is not 16 bit. It is signed 16 bit two's compliment.
You are concocting a story to fit in with your mistaken beliefs.
Are you saying it is not signed 16 bit two's compliment?
It is not signed.( Edit - it is signed, but it's two's complement)

https://en.m.wikipedia.org/wiki/Two%27s_complement
Last edited by Erin1 on 09 Nov 2019 11:07, edited 1 time in total.

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

Post by Erin1 » 09 Nov 2019 10:41

You're thinking about it wrong.
Irrespective of the polarity of the musical signal, or sine wave, the "snapshot" has 16 bits to represent the amplitude of the signal. Always 16 bits.

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

Post by NOYB » 09 Nov 2019 11:06

Erin1 wrote:
09 Nov 2019 10:38
NOYB wrote:
09 Nov 2019 10:26
Erin1 wrote:
09 Nov 2019 10:12


You are concocting a story to fit in with your mistaken beliefs.
Are you saying it is not signed 16 bit two's compliment?
It is not signed.
Can you please provide a source for that. Everything I've seen says it is signed.

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

Post by NOYB » 09 Nov 2019 11:07

Erin1 wrote:
09 Nov 2019 10:41
You're thinking about it wrong.
Irrespective of the polarity of the musical signal, or sine wave, the "snapshot" has 16 bits to represent the amplitude of the signal. Always 16 bits.
Right.

0000 0000 0000 0001 to 0111 1111 1111 1111 (+1 to +32767)
0000 0000 0000 0000 (0)
1000 0000 0000 0001 to 1000 0000 0000 0000 (-1 to -32768)

That indeed is 16 bits. Never been in dispute.

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

Post by Erin1 » 09 Nov 2019 11:08

Sorry, it is signed but it's two's complement

https://en.m.wikipedia.org/wiki/Two%27s_complement

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

Post by Erin1 » 09 Nov 2019 11:09

NOYB wrote:
09 Nov 2019 11:07
Erin1 wrote:
09 Nov 2019 10:41
You're thinking about it wrong.
Irrespective of the polarity of the musical signal, or sine wave, the "snapshot" has 16 bits to represent the amplitude of the signal. Always 16 bits.
Right.

0000 0000 0000 0001 to 0111 1111 1111 1111 (+1 to +32767)
0000 0000 0000 0000 (0)
1000 0000 0000 0001 to 1000 0000 0000 0000 (-1 to -32768)

That indeed is 16 bits. Never been in dispute.
From Wikipedia-
The two's complement of an N-bit number is defined as its complement with respect to 2N. For instance, for the three-bit number 010, the two's complement is 110, because 010 + 110 = 1000. The two's complement is calculated by inverting the digits and adding one.

Erin1
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Re: What is the dynamic range and S/N ratio of CD format?

Post by Erin1 » 09 Nov 2019 11:12

Im a qualified electronics technician. But It's been ages since I did this at school.
Unfortunately I'm not that great at maths and I don't do this stuff every day.

The two's complement explains where you've been going wrong.

I really hope this has helped.

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

Post by NOYB » 09 Nov 2019 11:17

Erin1 wrote:
09 Nov 2019 11:12
The two's complement explains where you've been going wrong.
How does two's complement explain that I'm going wrong?

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

Post by NOYB » 09 Nov 2019 11:20

Erin1 wrote:
09 Nov 2019 11:09
NOYB wrote:
09 Nov 2019 11:07
Erin1 wrote:
09 Nov 2019 10:41
You're thinking about it wrong.
Irrespective of the polarity of the musical signal, or sine wave, the "snapshot" has 16 bits to represent the amplitude of the signal. Always 16 bits.
Right.

0000 0000 0000 0001 to 0111 1111 1111 1111 (+1 to +32767)
0000 0000 0000 0000 (0)
1000 0000 0000 0001 to 1000 0000 0000 0000 (-1 to -32768)

That indeed is 16 bits. Never been in dispute.
From Wikipedia-
The two's complement of an N-bit number is defined as its complement with respect to 2N. For instance, for the three-bit number 010, the two's complement is 110, because 010 + 110 = 1000. The two's complement is calculated by inverting the digits and adding one.
Right. Not in dispute. What does that prove in regard to SQNR and dynamic range of the given data set?

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

Post by Erin1 » 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.