Frequency demodulation with a spectrum analyzer
The trick here is that the RBW filter is placed so that its transition band (on one side) spans the frequency range that the modulated signal covers, so the attenuation of the filter is dependent on the modulation signal.

The RBW must be selected so that the transition band is wide enough that the entire signal fits into one half of the filter, but typical RBW filters fall off quickly beyond their design 3dB bandwidth.

If you were to demodulate the center of the signal for the time domain view, you wouldn't see much of an amplitude change, since it's a frequency modulated signal, and what you see as a change in amplitude in the time domain view is really the shape of the RBW filter.