This says: each additional bit increases the signal-to-noise ratio by 6dB. The exact formula gives an SNR
of roughly 98dB for 16 bits and an SNR of 146dB for 24 bits (as opposed to 96 and 144 for the thumbrule).
Taking a sinusoid at full amplitude as reference signal is of course a rather optimistic assumption,
because this is a signal with a quite high power - its power is 1
2 and its RMS value therefore p1
2
= 0.707.....
You are probably familiar with the notion of RMS-levels in decibels: the unit amplitude sine has an RMS
level of −3.01dB in this notation - such a high RMS level will occur rarely for practical signals. Thus, we
would expect a somewhat lower SNR for practical signals. A practical implication of the above analysis is,
that when recording audio signals, we have to make a trade off between headroom and SNR. Specifically:
for each 6dB of headroom we effectively relinquish one bit of resolution