= Sub-step estimation with uniform dither
{title2=$\operatorname{Var}(\overline Q)=f(1-f)\Delta^2/N$}
Let a constant input lie a fraction $f$ of the way between two consecutive quantizer levels separated by $\Delta$. With independent uniform additive <dither> spanning one step and nearest-level rounding, the two output codes occur with <probabilities> $1-f$ and $f$. Their mean equals the input and their sample-average <variance> is the displayed expression. This simple model shows both the sub-step information and the remaining <noise> cost.
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