Quantization noise refers to the modeling of the difference between an analog signal and its quantized version as an additive noise process. The power of the quantization noise can be calculated by the assumption that the difference between the analog signal and the quantized signal is uniformly distributed inside the quantization level (the power is proportional to the variance of this distribution). Under this assumption, if you quantize to
N bits, with uniformly separated levels, you get that the signal to quantization noise power ratio is about
Now, so far I haven't spoken at all about frequency or spectrum, since the quantization noise is added to each sample of the signal without regard to the sampling rate, or the frequency of the analog signal itself.
A Sigma-Delta ADC is known to reduce quantization noise. The explanation usually involves talking about high-pass filtering of the noise, and stuff like that. But I don't understand how anything can change the power of the noise, as it is still true that the quantized signal has an error somewhere within the quantization level, and by definition of quantization you can't get a smaller error than that (maybe the answer is that Sigma-Delta ADC makes the error not uniformly distributed?). And how can the frequency domain help to analyze this?
I would appreciate to see a concrete worked-out example with numbers/parameters that show how the Sigma-Delta ADC operates on a given signal, giving low quantization noise.