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Coefficient Quantization

The coefficients in a band are all quantized with the same step size $Q$. To store $Q$ in the bit stream, it is indexed as
Q_i = {\rm round}(10\log(Q)+35),\ {\rm (min\ 0,\ max\ 50)},
\end{displaymath} (34)

and thereafter Huffman encoded. The $Q$ controls a nonuniform coefficient quantizer, with the following characteristic.
x_Q = {\rm sign}(x){\rm round}\left ( \left \vert \frac{x}{Q} \right \vert ^{1/c}
\right ),
\end{displaymath} (35)

where a $c=1.3$ has proved to work well. A nonuniform quantizer does not follow the masking threshold theories in section 3.4, but works very well -- it is used in e.g MPEG-2 AAC [7].

The coefficients of any orthogonal linear transform can be quantized as described above, since

$\displaystyle Qerr({\bf X})$ $\textstyle =$ $\displaystyle ({\bf X}-{\bf X_Q})^T({\bf X}-{\bf X_Q}) =
(U^T({\bf x}-{\bf x_Q}))^T(U^T({\bf x}-{\bf x_Q})) =$  
  $\textstyle =$ $\displaystyle (({\bf x}-{\bf x_Q}))^T(({\bf x}-{\bf x_Q})) = Qerr({\bf x})$ (36)

and so the quantizer makes no difference between the coefficients from the different modes in section 4.2.2.

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Download bosse.pdf

``An Experimental High Fidelity Perceptual Audio Coder'', by Bosse Lincoln<>, (Final Project, Music 420, Winter '97-'98).
Copyright © 2006-01-03 by Bosse Lincoln<>
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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