A lot of those signal jumps seem to be powers of 2, so you could have a timing problem.
IIRC DE0-Nano has an ADC with spi interface: if spi has poor timing, it could sample twice the same serial bit and skip the next one, and this would lead to something like that.
Does spi data from adc change on the right clock edge?
Another common problem could be you are exceeding adc max conversion rate, then it returns you partial converted data. This is more probable if you are cyclicing on multiple adc inputs and you don't wait the required input selection delay.