In oversampled A/D the idea is to take more samples per unit of time. If we assume that the error remains independent from the signal, we can achieve a better SNR by lowpass filtering the oversampled signal and downsampling in the digital domain:

• in the time domain, oversampled A/D corresponds to taking more samples than needed and then "averaging" them together via a lowpass filter. Averaging improves the SNR

• in the frequency domain, oversampled A/D results in a "useful" signal with a narrower spectral support, while the quantization noise remains full band. The lowpass filter eliminates the out of band noise, thereby improving the SNR

In oversampled D/A we use digital oversampling to create extra "room" in the digital spectrum (the spectrum "contracts"). After interpolation to continuous time using a non-ideal interpolator there will be spurious frequency content in the analog spectrum at multples of the interpolation frequency. The extra gap created by oversampling allows us to use an analog lowpass filter after D/A with a much larger transition band, that is, a much cheaper filter.