Low Pass filtering in Delta Sigma modulation

adc

I was reading about delta sigma modulators. I read that to make the data more accurate it performs digital low pass filtering on the quantized data. So like, if we have a one bit quantizer which is pushing data out at some rate, let's assume that its a DC signal,and we take average after every four samples we increase its accuracy to 2 bits. Similarly, if we take the average every 16 samples we increase it to 4 bits.
For a single bit quantizer, it makes sense since adding 4 one bit values would result in 4 different results which could be expressed in 2 bits. Firstly, is this reasoning correct?
But suppose instead, I have a 2 bit quantizer, and I average every 4 samples, what should be the resolution of the resulting output data?
Here is the link from which I was reading:
http://ewh.ieee.org/r5/denver/sscs/References/2002_07_Analog_AN-283.pdf

Best Answer

If you averaged 4 samples from a standard ADC connected to a source that has band-limited (but spectrally flat) white noise then you would increase the resolution by 1 bit. This is the standard approach.

But, you are talking about a sigma delta ADC and the returns are much better than one-bit per four samples because this type of ADC produces quantization noise that is much greater at higher frequencies thus, averaging is much more effective.

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(source: eet.com)