Agilent Technologies 93000 SOC Series Training Manual page 555

NOTE
Example:
Averaging by Waveform Repetition
Oversampling
Oversampling is a method to increase the measurement accuracy.
This method is also based on averaging.
Assume you need to measure the signal-to-noise ratio of an 18-bit
audio DAC that is operated at a conversion rate of 48 kHz.
However, your waveform digitizer has only a resolution of 16 bits.
So what to do?
In any case, you will first limit the output signal spectrum to the
1
Nyquist frequency of the DUT, that is 24 kHz, by choosing an
appropriate anti-aliasing lowpass filter.
If you would now capture the output waveform with a sampling
frequency of 48 kHz, the result would have an accuracy of 16 bits,
which will not suffice to accurately test an 18-bit DAC.
The solution is oversampling:
2 Digitize the output signal at a rate of 16 times 48 kHz, that is
768 kHz.
Then average the 16 data points of each level.
3
The resulting sampling frequency is 48 kHz. But averaging 16 data
points increases the resolution by the square root of 16, which is
4. A factor of 4 means 2 more bits.
The increase in accuracy is always the square root of the number of
averaged data points.
Appendix A
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