On oversampling of quantization noise

This is about Eq.(3) of [Candy'92]. Basically, I keep asking myself why the sampled quantized noise spectral density is given by


where the quantization noise is a white process with the following RMS value:


[Candy'92] explains that due to sampling, the noise power folds into the frequency band

However, I have to find a self-convincing explanation.

Here is how I understand the impact of oversampling on quantization noise:

1- we should consider a LPF with the bandwidth of

2- the sampling/quantization system is as follows [x denotes the instantaneous quantization noise]:

x--|sampler|--|LPF: h[n]|--y



3- Auto-covariance of LPF output is given by:


4- for a ideal LPF with f_0 = f_s/2, we have



5- Consequently the density of the quantization noise, which spreads over

is given by