if understand correct....
You need a microcontroller who, is fast enough, to proccess your signal.
most important , you must take attention to D/A to be that fast.
since D/A most propably will be slower than MCU.
as dknguyen mentiom your pulses must be 18us.
but i also noted that not all pulses have not the same width, ie first is 90(ns ?) second is 45(ns ?) etc.
Anyway to found how fast your D/A must be , you should take smallest pulse , in your case 18(ns ?) , transorf it to Hz ie 1/0.000000018= 55.55 MHz and you found it ,
You D/A must be able to generate MINIMUN 55.55 Million samples per second (aka 55.55msps).
Note that this speed is quite fast, and achieved with realy fast mcu most propably you you will need a ARM based cpu at 60mhz clock rate. propably way more to have time to proccess output too 100/150mhz !?
if it not ns but us(mikrosecond) the its not 55megaherz but 55.55KiloHerz which is possible with vast majority of mcu out there AVR,PIC etc