Jose,
Thank you very much for your fast response. While I wasn't able to solve my problem, your suggestions have helped to narrow the scope of the problem and hopefully will eventually lead to a solution.
Jose> The easiest way to reduce noise issues you are hearing would
Jose> be enabling the ADC_HPF_FREEZE bit (bit 1) on the
Jose> CHIP_ADCDAC_CONTROL 0x000E. [...]
I tried this. The freeze function was definitely working because the ADC responded to DC, whereas normally DC is filtered out. Unfortunately, though, the noise did not change.
Jose> A general recommendation [...]
Jose> Series coupling capacitors [...]
Jose> an LC filter [...]
Generally these are good suggestions, but I have found that the noise is still present even when all input drive is removed from the ADC inputs. (A 1 nF capacitor to ground is the only connection to each input.) To me, this demonstrates that the noise is internal to the ADC itself.
Strikingly, only the left input is noisy, which lends credence to the idea in the previously referenced discussion thread (https://community.nxp.com/message/505328) which suggests that the microphone input circuit is involved. One way or another we have two inputs that do not behave identically -- one is noisy, the other is quiet -- and since all input drive has been disconnected, the CODEC itself is implicated... unless I am missing something.
Gratefully and hopefully,
David