Electron cyclotron emission (ECE) from hot tokamak plasmas is recognized nowadays as a very informative diagnostic of main plasma parameters. Among several instruments developed to measure ECE, only a Martin-Puplett interferometer operates in a broadband frequency range of ECE from 70 to 1000 GHz. To derive the absolute radiation temperature of the plasma, a total measurement system, including front-end radiation collection, a transmission line, and the interferometer, is calibrated using a hot/cold calibration source. It takes a long time to calibrate the ECE system because of the high values of the noise equivalent power (NEP). A new technique, Hilbert-transform spectral analysis, is proposed for ITER plasma ECE spectral measurements. The operation principle, characteristics, and advantages of the corresponding Hilbert-transform spectrum analyzer (HTSA) based on a high-Tc Josephson detector are described. Because of the lower NEP values of the Josephson detector, this spectrum analyzer might demonstrate shorter calibration times than those for the Martin-Puplett interferometer. Because of a principal difference between Fourier and Hilbert transforms, the HTSA might have an additional advantage in retrieving harmonic ECE radiation from a continuous thermal background.