A modern radar gun operates in the Ka-band, Google says between 33.4 and 36 GHz. Assuming 12 bit samples, your proposed solution needs to process a minimum 3.9 gigabits per second, or ~500 megabytes per second. To do this work in software would require a workstation.
Not to mention I'm not even sure if you can operate most ADCs above the 1st Nyquist zone like would be needed here.