SQNR

SQNR, or signal-to-quantization-noise ratio, is a measure of the fidelity of a digitally quantized signal. It compares the average power of the intended signal to the average power of the quantization error introduced by a quantizer or ADC, and is usually expressed in decibels as SQNR = 10 log10(P_signal / P_noise).

For a uniform N-bit quantizer with a full-scale sine input, assuming the quantization error is uniformly distributed and uncorrelated with the signal, the noise power is Δ^2/12, where Δ is the step size. If the full-scale amplitude is A, then Δ = 2A/2^N and the signal power is A^2/2. This yields SQNR_sin ≈ 6.02N + 1.76 dB. The 6.02 dB per bit reflects the logarithmic scaling of power with bit depth.

If the input does not use the entire dynamic range, with peak amplitude a = αA (0 < α ≤ 1), then the signal power scales as α^2, and SQNR(α) = 6.02N + 1.76 + 20 log10 α dB. In practice, actual SQNR depends on the signal’s crest factor and distribution; the sine-case provides a commonly cited baseline.

Examples: an 8-bit quantizer yields about 49.9 dB of SQNR for full-scale sine input, while 12-bit yields about 74.0 dB. Additional factors such as dithering, noise shaping, and nonuniform quantization can modify the effective SQNR in real systems.