Quantization in digital filters

We quantize like this

$$\hat{x}[n]=Q[x]$$

Where $Q$ is an unlinear function

Instead of modeling it as an unlinearity, we model it as a linear function

$$\hat{x}[n]=x[n]+e(n)$$

Where $e$ is an uniformly distributed random variable between $-\frac{1}{2}$ and $\frac{1}{2}$

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