Sure, you can do all that in an FPGA if you like.
You're FPGA design would consist of three major parts:
1. the ADC/detector timing generation and sample acquisition
2. the floating point arithmetic
3. the external processor interface
Are you looking for pointers to "getting started" tutorials etc. or did you already have some specific questions?
Since the title of the thread you created is "floating point math", here is a pointer to the Altera-supplied floating point arithmetic modules, which are free to use:
http://www.altera.com/literature/ug/ug_altfp_mfug.pdf The core of your algorithm would likely consist of simply chaining together the correct series of blocks. i.e. your STM32F4 MAC instruction would require the ALTFP_MULT followed by ALTFP_ADD_SUB with necessary glue logic and registers in between.