If that is the case, these spurs should move to a different frequency when you run an FFT with 200MHz bandwidth, because I expect the sample rate will then be 400MS/s, which is not dividable by 31.25. Or does is sample at 500MS/s and throws away a bit of the FFT?
Could you post a plot to 200MHz to check this with your 5444B?
PicoTech have pioneered the fully digital trigger system, which requires the ADC to run at full sample rate all the time. This sample data stream is fed into the digital trigger system. Only after that, the sample data get decimated if required to fit shorter record buffer lengths, so we get the effective sample rate at this point.
In other DSOs, where the FFT is not a completely independent operating mode like it is for PicoScopes, one additional decimation step is required whenever the max. FFT length is less than the record length.
Apart from that, the old 3206B samples at 500MSa/s and the FFT shows quite a few strong spurs, starting at 31.25MHz again. That’s probably just the frequency of the clock generator signal, which is then multiplied by a PLL in order to get the required ADC sample clock.
See the noise plot from 1kHz to 200MHz:
Pico 3206B FFT 50Ohm 1kHz-200MHz
EDIT: Please keep in mind that this plot is not directly comparable to the 4000 and 5000 series, because the most sensitive input range is +/-50mV (10mV/div) for the 3206B.