In article 20031121215550.28390.00000721@mb-m14.aol.com, BobGardner at
bobgardner@aol.com wrote on 11/21/2003 21:55:

>> 
>> If I am given a 16-bit fixed-point number of uniform quantization, I
>> can surely say that the maximum theoritic dynamic range I can get is
>> 96.329 dB 
> 
> Minor quibble... 96 dB is 6 dB per bit for 16 bits...the max signal is really
> +-32767 or +-15 bits, right? so its 90dB....

but the quantization error is really +or- 1/2 (if full scale is +or- 32767).
so the ratio is still 2^16 if the p.d.f. of the signal and quantization are
the same (both uniform).  then the dynamic range (S/N in dB plus dB of
headroom) is 6.0206 * 16 = 96.33 dB.  if there is a constant dB term in the
formula relating bits to dB, then there is some difference in the p.d.f. of
signal to noise (signal might be sinusoidal, noise remains uniform p.d.f.)
or there is more to the model (like non-uniform quantization, nonlinearity).

r b-j