Bridging of the terahertz gap in the electromagnetic spectrum between the microwave and infrared ranges requires a variety of new technological developments from basic elements, such as emitters and detectors, to complete systems, such as spectrum analyzers and imagers. As an example of these developments, Hilbert-transform spectral analysis of terahertz radiation sources has been demonstrated. A spectrum analyzer based on a high-T c square-law Josephson detector has been developed and characterized in the frequency range from 50 to 1800 GHz. Spectra of output terahertz radiation from optically-pumped lasers and frequency multipliers have been studied, and their regimes were optimized for a single-frequency operation. Starting from the optimized multipliers, a polychromatic source has been synthesized and characterized with Hilbert-transform spectrum analyzer.