Quantization Levels and Dynamic Range

[percy]

I understand that 16 bits can represent 65536 unique amplitude levels. Now dynamic range is defined as the difference between the maxiumum and minimum levels that can be represented.
Lets say that the minimum level is 0 and maxium level is 65536, so the dynamic range is 96.3db, or so I have read/heard in most places.

However, although 16-bit does mean 65536 unique quantization levels, it is actually +32767 to -32767, so the maximum swing on each side of 0 is really only 32767. So why is the dynamic range based on 65536 levels of quantization and not 32767 ?

Shouldn't the dynamic range of the 16-bit audio cd then be only 90.3db ? (that too only theoritically, would be still lower practically). Its like asking - is the dynamic range based on the peak signal level or the peak-peak signal level ?

Am I thinking this through correctly ? or am I missing something big here ?

[Bernhard]

Music is AC signal so peak-peak.

[percy]

but in any other AC signal db gain/difference calculations - for example voltage gain - the voltage that is being referred is not p-p.

[ghetto]

I'm not really sure how to explain it other than, the signal is still being described by 16 bits, so it doesnt matter if part of the signal goes below "0 volts" ... its still 96dB.

[poynton]

Originally posted by percy
.............
However, although 16-bit does mean 65536 unique quantization levels, it is actually +32767 to -32767, so the maximum swing on each side of 0 is really only 32767. So why is the dynamic range based on 65536 levels of quantization and not 32767 ?...................

Hi

It is not an AC signal !

The levels go from 0 - 65536

They are just offset in some DACs

Andy

[SY]

Originally posted by percy
but in any other AC signal db gain/difference calculations - for example voltage gain - the voltage that is being referred is not p-p.

Not exactly. Gain RMS is the same as gain peak is the same as gain peak to peak. For example, let's say I have a box with a gain of 10. Then 1V RMS in gives 10V RMS out. 1 V p-p in gives 10V p-p out. And so on and so on.

[phn]

Scuse me, but is peak to peak applicable here? We're talking "ones" and "zeros"--2^16--here, aren't we?

[SY]

Yes it is. We're talking about signal peaks. The question really is, is RMS applicable here?

[moamps]

Originally posted by percy
....although 16-bit does mean 65536 unique quantization levels, it is actually +32767 to -32767, so the maximum swing on each side of 0 is really only 32767....

Hi:

The minimum swing isn't 1bit on each side (two bits). It's just 1 toggling bit (half bit on each side ). The toggling bit may represent a converted sine signal with 1bit peak-peak value, for instance.
So, if the signal's minimum value is 1bit peak-peak and the maximum value is 65536 peak-peak, the dynamic range is 6.02*n or 98dB for n=16. Theoretically, the dynamic range is even higher for 1.76dB (sine signal). In practice, 90dB is a more realistic value.

Regards,
Milan

[phn]

Originally posted by SY
Yes it is. We're talking about signal peaks. The question really is, is RMS applicable here?

It was in that line I was thinking. Maybe I'm stumbling on the semantics.