Re: ADC sampling
In your system, I assume you have a microphone amplifier preceding the ADC. You can still use the traditional low frequency ADC (a few tens of kHz) to do a nice job, if the Mic amp has a fully differential structure which features in high PSRR. But since the ripple you have on the supply has frequency as high as 10MHz, the Mic Amp may not have sufficient high PSRR at that frequency range. My suggestion is to have a clean regulator to regulate from this noisy supply and use this regulated supply to power your ADC's analog section of the circuitry. Another solution can be using a more clean supply for your ADC.
You can't just use a much higher sampling frequency to deal with the 10MHz supply ripple, as suggested by someone here. For a voice band application, even with sigma-delta oversampling ADC, you can only have sampling frequency as high as two to four Mega Hertz, not even close to the 10MHz ripple noise here.