After troubleshooting other designs where the A/D is noisey, I believe the biggest problem is a lack of a ground plane. EVERYONE has to agree on where ground is. Otherwise, the input to the A/D will have noise on it, and the noise will show up in the conversions.
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS says:
There are basically only two reasons why you want to include an anti-aliasing filter:
1. You are under-sampling the signal bandwidth, so there's signal power in frequencies above 1/2 the sampling rate. If you don't anti-alias, you will fold down the signal frequencies into lower harmonics, converting signal power above the Nyquist frequency into noise. An example of this would be, for example, audio input signal frequencies beyond 20 kHz, which can't be heard by the human ear. This is why CDs sample at 44 ksps (2x 20kHz + margin) and anti-alias the input to the adc. (This is what Harold and Mario and others are discussing.)
2. You are sampling a signal with wide-band noise added. If you don't restrict the bandwidth, the noise glitches (which may be rail-to-rail in size) will get sampled as the signal, and you'll get adc output glitches with a significant number of bits in error. By limiting the bandpass to the adc input, you reduce the noise dramatically. (This is what I've been discussing.)
The only reason you would not filter the input to an adc would be that the input has the following characteristics:
a. Signal bandwidth very low (e.g., DC voltages, or 10x over-sampling).
b. No noise present.
Usually it's (b) that drives you nuts in the end. There's plenty of noise sources present in a digital system with wires and sensors.
A good design rule is to never allow more bandwidth than you really need.
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