We propose a novel (to our knowledge) and simple real-time optical monitoring (RTOM) system for dynamic spectral analysis of telecommunication signals, involving electro-optic (EO) temporal sampling followed by dispersion-induced frequency-to-time mapping and high-speed photodetection. This system enables tracking of the presence and relative intensity of multiple wavelength-division-multiplexed (WDM) data streams that span over a broad frequency band with high resolution, accuracy, and fast measurement update rates. We derive the design conditions and trade-offs of the proposed scheme and report proof-of-concept experiments and a numerical result that demonstrate successful spectral monitoring of dense-WDM signals with different modulation formats and bit rates, over the full C-band, with the needed resolution to discern channels separated by a few tens of GHz, and with an unprecedented fast measurement update rate in the MHz range.