Signal power and spectrum analyzer
The actual measurement of Spectrum Analyzers is "power / filter bandwidth".

Your spectrum analyzer has a filter bandwidth that you can typically configure. For example, if your filter bandwidth is 10 kHz and you measure -12dBm, that's -12 dBm/10 kHz = -12 dBm - 40 dBHz = -52 dBm/Hz.


  why is it frequency dependent?


Because you're using a spectrum analyzer! 

The SA's job is to tune through your band of interest: stop at a frequency for a period of time, measure what power is coming through a filter, tune to the next frequency, measure, repeat. That way, you get a Power Spectral Density estimate for different frequencies.

I don't which bandwidth you're currently using, but it's probably less than your signal bandwidth, and hence, you don't measure all the energy, but just a part of it.