Power supply noise problem in a measurement system
To re-formulate the question, the system has the following structure:


a bunch of pressure sensors are combined into analog block "ZOC33", with addressable multiplexor into a single analog output;
The block "RADBASE" contains ADC to USB1.1 converter.
The analog link between ZOC33 analog muxer and the ADC is 10ft (3m) long. While the analog link does have a separate analog ground (-OUT) that is separate from digital and power return ground, the +OUT analog line does not have any shield.


The system seems to be distributes over an area of 20-30ft, and the overall grounding wiring is missing.

The max scale output is +-2.5V, and the observed episodic "noise" is 100mV (as compared to presumed "normal" 20mV), or about 4%, which is too much for (I guess) a 12-bit ADC.

My guess is that the problem is related to unprofessional ground wiring across the whole data acquisition system, which has ground loops, and thus is susceptible to external interference from some heavy electrical equipment (motor/pumps, welders, etc.) nearby, or radio emissions. The correlation between noise on power rails and noise in ADC channels is likely because the entire system receives EMI, and all grounds are bouncing everywhere. 

Solution to the problem is to hire a seasoned professional engineer to examine the entire setup, check/monitor quality of AC supply network, identify sources of high-power EMI, and suggest correct grounding schema (or power filters on AC) for the entire data acquisition system.

P.S. From the power spectrum of noise (FFT picture), it looks like the building has some poorly designed switching high-power supply unit running at 80kHz, with extremely sharp edges. And sitting on Floor2 AC mains.