Sometimes things just don't make sense! For instance, your RC filter or amplifier's lowpass filter at the input of a delta-sigma ADC can produce a noisier digital output. Didn't you design the filter to reduce noise so that you'd get more instead of fewer noiseless bits from your converter? It is as easy to eliminate higher-frequency noise with an analog lowpass filter as it is to inject noise into the frequency band below the corner frequency of your filter. If your filter produces noise in the frequency band of interest, your conversion output results will be noisier than you might expect.
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