To generate the quantisation noise, we follow this recipe:
First, we generate using a random uniform distribution:
$$U_k^*\sim U\left[ {0,1} \right]$$Then, we multiple the sequence by $sqrt(12)$ so:
$${U_k} = \sqrt{12} U_k^*$$
Next, we find the derivative of $U_k$
$${{\dot U}_k} = \frac{{{U_{k + \Delta t}} - {U_k}}}{{\Delta t}}$$
In this case, we modify the derivative such that:
$U_k^. * (delta)t = U_{k + (delta)*t} - U_k$
Thus, we end up with:
$${x_k} = \sqrt Q {{\dot U}_k}\Delta t$$
$${x_k} = \sqrt Q \left( {{U_{k + 1}} - {U_k}} \right)$$