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Digital Microphone PCM Offset?

I'm decimating a digital microphone PDM output using the ADC3101.  I'm seeing a 1K-2K offset in the output PCM samples.  If I apply digital gain (for software reasons), the resulting PCM samples can become quite unbalanced and end up clipping against one of the rails (+/-32768 in my 16-bit case).

I'm considering implementing a HPF in the ADC3101 on-chip filtering hardware block.  I could also compute a running average in software and remove the offset but I will lose a few MIPs from my CPU.  Unfortunately we have one algorithm that is zero-crossing dependent so offset is an issue for us.  We have other algorithms that are frequency based and they work fine with some offset as long as we don't clip.

Has anyone else hit this issue and what was your solution?

Thanks, Chris