recently I meet a problem.
I generate a random Gaussian signal $x$ with mean $0$ in MATLAB. And use a $4$th lowpass Butterworth filter to acquire $x'$. Then I use the binary rounding quantization method to get the quantized signal $x''$. And I find that the Fourier spectrum (FFT) of $x''$ contains some high-frequency information. That means some energy leaks to high-frequency regions after quantization.
Also, I find the energy in high-frequency areas is related to the bandwidth of the filtered signal $x'$. When the bandwidth of the filtered signal $x'$ is relatively low, the energy of the high-frequency areas of the quantized signal $x''$ is also lower. I find that some historical references about the assumption of the whiteness for quantization noise. But it seems that this is not the case.
Do you all meet this question? Could anyone give me references for this problem? Thanks in advance!