We describe a method to determine the radiation spectrum of terahertz sources using a transmitted Fabry-Perot interferometer and a bolometer detector. Our novel Fabry-Perot spectrometer can measure the spectrum of an unknown broadband sub-terahertz and terahertz source. The spectrometer does not need to be pre-tuned. We develop a new algorithm to support the measurements using this spectrometer. Our technique allows us to measure the spectrum over more than an octave, and our numerical algorithm is very stable and robust, providing for an accurate spectrum determination. Two Gunn oscillation sources with the main frequencies at 200 GHz and 600 GHz are used to test the proposed method. The spectrum extracted from the measured data shows that this method is accurate and reliable.