Rydberg atoms have extremely large polarizability and transition dipole moments, allowing for non-destructive and traceable precise measurement or communications over ultra-broadband electromagnetic signals by the Autler-Townes splitting effect in the resonance region and the alternating current Stark (AC Stark) shift effect in the off-resonance region. In a cesium vapor cell at room temperature, by varying the coupling laser wavelength, three energy levels 70S1/2,42D5/2,and30D5/2 are selected to measure the spatial electric field strength of electromagnetic signals in the far-off-resonance region (2 GHz) and the resonance region (9.953 GHz and 29.54 GHz), respectively. On this basis, the attenuation factors caused by environment scattering and vapor cell perturbations are calculated. Meanwhile, the potential of Rydberg atoms for communication applications in the broadband frequency range is demonstrated by experiments on the variation of the signal-to-noise ratios (SNRs) of electromagnetic signals with different modulation frequencies under amplitude modulation and frequency modulation in the far-off-resonance region (2 GHz), near-off-resonance region (9.5 GHz), and the resonance region (29.54 GHz). Furthermore, for the amplitude modulation signal with a modulation frequency of 10 kHz, the demodulated signal SNR is investigated in the ultra-broadband frequency range of 100 kHz-40 GHz. The experimental results reveal that Rydberg atoms can break the operational bandwidth limit of conventional electronic sensors, and have the ability of electric field sensing and communications in the ultra-broadband continuous spectrum range.