A spectrum analyzer records a signal digitally for a period of time, then Fourier transforms it. It might also be set to average many such spectra together, or to record the peak amount of power seen at each frequency.

It measures whatever you want it to measure. If you want it to record what’s in the air, you stick an antenna in the air and take that as your input. If you want to see what’s coming off a transmit antenna, you stick your probe antenna in front of the transmit antenna. Maybe you want to see how well a filter is doing in your receiver at filtering out unwanted parts of the spectrum. So you hook it up before and after the filter and compare the spectra in those two places.”