How do you simultaneously undersample and oversample?
Undersampling is also known as &quot;bandpass sampling&quot; and &quot;IF sampling&quot;.  Consider the sampling of an 11 Hz sine wave and a 1 Hz sine wave, both sampled by a 10 Hz sampling clock as in the figure below:
The samples that are produced (the red circles) for both waveforms are identical. Thus the 11 Hz &quot;Intermediate Freuency&quot; or IF has been downconverted in the sampling process to 1 Hz. We can use this technique to undersample a bandpass waveform, and thereby down-convert it at the same time (putting our waveform of interest in the first Nyquist zone: ±$F_s/2$ where $F_s$ is the sampling freqquency).  A key requirement that satisfies Nyquist is that the sampling rate used must exceed twice the bandwidth of the signal (note I said bandwidth, not highest frequency!).
That is &quot;Undersampling&quot; as most often described. To oversample a waveform, we sample at a rate significantly higher than the Nyquist criteria, with one motivation to increase the SNR as limited by quantization noise (by sampling hgiher, the same quantization noise is spread over a wider digital frequency, which we can subsequently filter down to our bandwidth of interest and thereby eliminate a significant amount of the noise).  Therefore to both undersample and oversample a waveform, we choose a sampling frequency that is significantly larger than the signal bandwidth (thus oversample), and then use a multiple of this sampling clock to down-convert the waveform of interest positioned at a higher IF frequency (undersample).
For example, consider a waveform that occupies 10 KHz of BW that resides at 20.25 MHz. If we sample this with a 10 MSps sampling clock, we would be both undersampling and oversampling at the same time. (The undersampling creates a digital waveform with 10 KHz of BW at 250 KHz, which is oversampled at 10 MSps).