Think about noise shaping spectrum and the way you cut the noise power with the decimation filter. It will give you the answer on the SNDR improvement. Technically you can push the BW of your decimation filter towards the lower frequency and have a better SNDR. SNDR anyways is limited to the input thermal noise of your ADC and also probably the phase noise of your VCO. The other thing is you should not compare the output of your ADC with /without decimation filter. Technically speaking the output of your ADC is the output of the decimation filter and you have to compare it with your input. Note that in the oversampled noise shaping ADC, the whole package (modulator followed by the decimation filter) is called ADC.
I do not understand 'Secondly, it is enough to use just a low pass filter without downsampling?" If you are using the CIC filter it basically includes the down-sampling process. CIC stands for Cascaded Integrator-Comb and have look at its structure. The first order CIC is an accumulator followed by down sampler and a differentiator.
zahramoh wrote on Nov 20th, 2020, 9:10am:I have used a decimation filter after the differentiator as you already mentioned, and the number of data decreased (exp: 1024 data were converted to 128 data by a 8 down sampler). So, I have some questions. Firstly, I was wondering if the sndr improves after the decimation filter? In other words, when I converted the digital data after the dicimation filter to analog signal, it was excelent, but I am not sure about the SNDR improvement.
Secondly, it is enough to use just a low pass filter without downsampling?