SQNR (signal-to-quantization-noise ratio): definition

Beginner

A score for how close a rounded copy is to the original: higher is better.

Novice

The ratio of the signal’s power to the power of the rounding error, in decibels (dB). Every extra bit of precision adds about 6 dB, which means roughly halving the error.

Expert

$10 \log_{10}\!\big(\sum x^2 / \sum (\hat{x} - x)^2\big)$ . For a uniform quantizer the noise power is $\Delta^2/12$ , so each added bit ( $\Delta$ halved) adds $20 \log_{10} 2 \approx 6.02$ dB. For floats SQNR depends on mantissa bits, not magnitude, as long as values stay in range.