What use would a D flip-flop being fed an analog signal have?
The output goes high if the input exceeds one value, and goes low if
  the input deceeds a lower value.


That sentence describes a Schmitt trigger: -



Top signal is the input. Middle single is a normal comparator output. Bottom signal is the Schmitt trigger output - notice how it switches high when the analogue input passes the high trigger threshold and only returns to a low output when the analogue input falls below the low trigger input value.


  The analog input is sampled at fixed intervals.


That implies a sample and hold circuit: -



It sounds like you are describing a schmitt trigger being fed from the output of a sample and hold circuit that, in turn, is fed from the analogue input.


  The output of the system is a single bit.


Yes it is, agreed.