Signal to Quantization Error (SQNR)

When noise is a result of quantization error, we determine its audibility using the signal-to-quantization-noise-ratio (SQNR), determined by the ratio of

• the maximum amplitude ($2^{n-1}$) to
• the maximum quantization noise (1/2 for a linear converter).

To determine audibility, the SQNR is provided in decibels (dB):

$$20\log_{10}\left(\frac{2^{n-1}}{1/2}\right) = 20\log_{10}\left(2^n\right)$$

$$= n \times 20\log_{10}(2)$$

$$\approx n \times 6$$

$$\approx 96 .$$