It could probably be handled by the realtime cores on the BeagleBone Black's SoC, or perhaps by an XMOS part, but if someone already knows how to develop for FPGAs there's not much of an incentive to try to shoehorn the task onto a microcontroller.
Anything that involves reading from moderately-to-insanely fast ADCs is a natural FPGA application, especially if multiple channels are involved.