pulsed signal spectrum analysis
Obviously!
Spectrum analyzer is like a power meter with a bandpass filter in front of it. If the bandwidth of the bandpass filter is too small, you do not let all of the RF power be detected. To complicate things, the center frequency of the bandpass filter is constantly changing, so if a pulse occurs when the bandpass filter is not tuned to that frequency, you again do not measure any power.
The first thing that you might want to do is set the analyzer so it is cenetered on the frequency desired and not sweeping. Then increase the RBW until you see no increase in signal power detected.
VBW just filters out changes (like pulsing power), so you want this set as wide as possible.
Average vs peak? Depends on the analyzer. Some only measure average, some can do both. Read the manual.