A prototype of Hilbert spectrometer for operation with pulsed far-infrared radiation has been developed and characterized. The prototype consists from a high-T, Josephson detector in an optical cryostat, analog electronics with a bandwidth of 14 MHz, and a DSP-based data acquisition system. The spectral range of the spectrometer can be as broad as 30 - 1200 GHz at the junction temperature of 78 K and can be shifted to the higher frequencies by lowering the junction temperature. Tests have been carried out using pulsed 94 GHz radiation with pulse duration of 200 ns and a pulse repetition rate of 1 MHz. A measurement time of 7 ms for a data set of 512 spectral points has been realized. It has been demonstrated, that in broadband (10 MHz) measurements without integration the developed spectrometer could operate in a power dynamic range of FIR radiation of 17 dB, which could be further enhanced by using integration functions.