Wideband Passband RF filter
I think you need to talk to a filter vendor instead of stackexchange.  For 4GHz you'll probably need some form of waveguide resonator-based bandpass filter.  But I don't know if you can get that wide of bandwidth with such a steep 50Mhz transition band without paying a small fortune.  Here's an IEEE article on a 4Ghz 500Mhz BP filter.