Yes,  and it can be quite easy to do.   A friend whipped one out in day.   Has 
16 inputs (used to be 8 inputs) and time stamps any selected edge transition 
and queues up the time stamp counter/channel values which get written into a 
bigger RAM buffer queue which gets periodically dumped out via USB.   The 
master counter runs at 100 Mhz (used to be 80 MHz) so the time stamps have 10 
ns resolution (all that was needed for his application).    The later version 
also decoded a GPS time stamp input for absolute timing.  Alas, again, it was 
developed for a paying customer so he can't share the exact design...  I've 
been trying to get him to sell a commercial version... it's a really slick and 
handy device.

--------------------

> My straw man would be a FPGA.  The idea is to collect a batch of pulse 
arrival times and DMA them into memory.  When the buffer fills up or a timer 
expires, it would finish that block and switch to the next one.  You could 
feed a PPS to the FPGA if you want timing linked to the outside world rather 
than just relative times.
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