We have demonstrated the first applications of Josephson-effect-based Hilbert-transform spectral analysis using high-T/sub c/ Josephson junctions. YBa/sub 2/Cu/sub 3/O/sub 7-x/ grain-boundary Josephson junctions have been fabricated on [110] NdGaO/sub 3/ bicrystal substrates for these measurements. At first, spectra of Josephson radiation have been measured by the Hilbert-transform technique in the range 60-800 GHz. A Lorentzian shape of the Josephson radiation and the possibility to obtain a spectral resolution as low as 0.1 cm/sup -1/ in the submillimeter-wave range has been demonstrated at liquid nitrogen temperature. Moreover, spectra of high-harmonic content of the radiation coming from commercial millimeter-wave oscillators have been measured in the spectral range from 60 to 450 GHz. A comparison of Hilbert-transform spectral analysis with conventional techniques is given.