Weird samples from SAR ADC
OK - I solved the problem. In my SPI setup for the microcontroller, I changed both the clock polarity and the clock phase and it solved the problem. I now have very clean, smooth curves.

I makes sense now. The 16-bit words read out from the ADC were indeed not correct and contained both information from the previous word and the current. That explains both the periodicity and weirdness in the plots.

Thankfully both the DAC and ADC seems to work fine with the new clock and phase polarity, despite being from different manufactures :-)