A full-scale sine wave yields 1.76 dB more signal-to-noise than uniform signals

Evidence

These maximum signal-to-noise calculations are assuming that both the signal and noise have a signal probability distribution that is uniform; that is, all signal levels within the range of the quantizer are equally possible. If one assumes a sine wave input at maximum level, then the maximum signal-to-noise ratio is improved by +1.76 dB because a sine wave spends more time at higher levels. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2658

Categorization

• SHARE: The classic +1.76 dB sine-wave correction is exactly the sort of number an audio-engineering friend would appreciate in passing.
• DEFINE: Explains why the uniform-distribution assumption underlies these SNR formulas, framing the sine-wave case as an exception.