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

Posted:

**08 Nov 2019 01:40**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.

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.