The Rigol DSA1000 and DSA800 series spectrum analysers have demodulation capabilities.
Here are some hints that can optimize the demodulation output.
1. Use an antenna matched for the frequencies of interest
2. Set the center frequency of the spectrum analyser to the center frequency of the signal of interest. For example, of you wish to demodulate an FM signal with a carrier of 100MHz, set your spectrum analyser center frequency to 100MHz.
3. Select the proper demodulation type (AM for AM signals, FM for FM)
4. Enable the earphone or speaker on the spectrum analyser
5. Insert a 3.5mm stereo or mono earphone set into the 3.5mm headphone jack (DSA815)
6. Set the demodulation time to 1s
7. Set the RBW to 1MHz
8. Adjust the volume to a safe level. You can also tweak RBW to lock in signal.