[Edit answer moved from OP edit to "Answers" as per comment suggestion]
I'm trying to create a simple model of a signal chain (image sensor) that includes an ADC but I'm failing to observe quantization noise. I'm afraid I'm missing big points about quantization noise. [Will assume Matlab for pseudo code]
Let's assume that the input signal has a range between 0-1 Volts and the ADC has N bits with
LSB=1/2^N (eg 8 or 10).
My input signal average is centered in the range and let's assume that the standard deviation is a certain percentage of the ADC LSB (alpha):
I'm modeling the ADC as a quantizer like so:
I evaluate the noise of the quantized image as
Iq_std_meas = std(Iq)
If alpha>>0.5 then the signal swing is big compared to the LSB. I'm expecting to be able to model the output noise as
Iq_std_model = alpha+1/sqrt(12) but it seems that a better model is
Iq_std_model = alpha since the quantization error becomes insignificant.
If alpha<<0.5 I'm expecting to be able to model the output noise as such:
Iq_std_model = 1/sqrt(12) but obviously Iq_std_meas tends to 0 the lower alpha becomes.
Note that for any value of alpha I can observe quantization noise as 1/sqrt(12) by just taking:
It seems I can't measure the final noise as
Iq_std_meas = std(Iq).
What is the fundamental point that I'm missing?