Quantization Error (Linear Converter)

• When noise is a result of quantization error, audibility is determined using the signal-to-quantization-noise-ratio (SQNR).

• If amplitude values are quantized by rounding to the nearest integer (the quantizing level) using a linear converter, the error will be uniformly distributed between 0 and 0.5.

• The SQNR of a linear converter is typically determined by the ratio of
  1. the maximum amplitude ($2^{n-1}$) to
  2. the maximum quantization noise (0.5 or $2^{-1}$)
  and is expressed in decibels (dB) as
  

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

  $$= 96 n=16.$$ (2)

  
  

• A sound with an amplitude 40dB below maximum would have a SQNR of only 56 dB.

• Matlab uses 64 bits (double-precision floating point)--convert to 16-bit when using audiowrite.