GuidoK wrote: ↑16 Nov 2019 13:47

The aspect of signed data is covered in that article.

Not in reference to CD data. Only in reference to DSP etc.

GuidoK wrote: ↑16 Nov 2019 13:47

That there is no mentioning of the word redbook is no meaningful argument. The word redbook alone is not relavant (it is also not mentioned in your link from teledyne....)

The article from teldyne... actualy described the data. Singed 16-bit. It didn't cover two's complement. Though that does not change the dynamic range.

GuidoK wrote: ↑16 Nov 2019 13:47

Regarding the maximum magnitude of 65536, that is related to if the the absolute minimum is 0 (so the difference between the maximum value and the minimum value)

If the 'correct' maximum value is set at 32768, then the 'correct' minimum value is -32767, and the difference between those two is still 65536. The maximum value is 65536 higher than the minimum value.

Show the dynamic range of a sine wave expressed as db for that.

db = 20Log(max/min)

GuidoK wrote: ↑16 Nov 2019 13:47

The signed data doesn't result in that the maximum amount of musical information in the data becomes less. This is a result from that the signing method used is two's complement signing. The signing doesn't take up any information that can't be used for audio in the datastream. It's a very easy conversion which is usually used to make adding/subtraction/etc easier in computers and in PCM audio to virtualize a sinus oscillating around a zero.

This was already covered in this topic in page 2 by Erin1

Thats how I see it too.

If you have a different opinion on that then you have a different interpretation of what two's complement signing is than how its defined everywhere else.

There is so much wrong there. Started to go over it piece by piece but it's just to much wrong. So I'll just try to go through the numbers instead.

A maximum amplitude sine wave:

positive phase peak value: +32767 two's compliment: +32767

negative phase trough value: -32768 two's compliment: +32768

A minimum amplitude sine wave:

positive phase peak value: +1 two's compliment: +1

negative phase trough value: -1 two's compliment: +65535

It is difficult to paint the picture textually but try to visualize this. The two's compliment moves the negative phase of the sine wave up to the top half of the 16-bit range (32768 to 65535). Thus the maximum negative phase magnitude of -32768 is now represented as +32768 and the minimum negative phase magnitude (-1) is represented as +65535. A range of 32767 (65535 - 32768 = 32767).

Each phase of the sine wave is still contained in a range of 32767. 0 to 32767 for the positive phase and 32768 to 65535 for the negative phase.

To change the level by 6.0206db, BOTH the positive phase AND the negative phase has to be changed by a factor of 2.

So when a -0dbFS sine wave is reduced by 6.0206db, it's positive phase peak value becomes 16384, and it's negative trough value becomes 49152 (32768 + 16384).

There are 15 such 6.0206db steps available.

15 x 6.0206db = 90.31db = 20Log(32768/1) = 20Log(2^15/1) = 20Log(max/min) = db

To illustrate:

sine wave at:

-0db: positive phase value: +32767 and negative phase value: -32768 (+32768)

-6db: positive phase value: +16384 and negative phase value: -16384 (+49152)

-12db: positive phase value: +8192 and negative phase value: -8192 (+57344)

-18db: positive phase value: +4096 and negative phase value: -4096 (+61440)

-24db: positive phase value: +2048 and negative phase value: -2048 (+63488)

-30db: positive phase value: +1024 and negative phase value: -1024 (+64512)

-36db: positive phase value: +512 and negative phase value: -512 (+65024)

-42db: positive phase value: +256 and negative phase value: -256 (+65280)

-48db: positive phase value: +128 and negative phase value: -128 (+65408)

-54db: positive phase value: +64 and negative phase value: -64 (+65472)

-60db: positive phase value: +32 and negative phase value: -32 (+65504)

-66db: positive phase value: +16 and negative phase value: -16 (+65520)

-72db: positive phase value: +8 and negative phase value: -8 (+65528)

-78db: positive phase value: +4 and negative phase value: -4 (+65532)

-84db: positive phase value: +2 and negative phase value: -2 (+65534)

-90db: positive phase value: +1 and negative phase value: -1 (+65535)

-oodb: positive phase value: 0 and negative phase value: 0 (0)

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

The values in parenthesis are the two's compliment of the negative phase values. The two's compliment does not change the number of 6db steps that exist in each phase. It simply makes the negative values positive for more efficient arithmetic processing.

oo represents infinity