Definition (Uniform Quantizer)

An $N$-level uniform quantizer over the interval $(a,b]$ has the following properties: $$\begin{align*} R_{i}&=(a+(i-1)\Delta,a+i\Delta]\\ y_{i}&=a+\Delta\left( i-\frac{1}{2} \right)\\ \Delta&=\frac{b-a}{N}\\ D(Q)&=\frac{\Delta^{2}}{12} \end{align*}$$