Provided is a Fourier transform spectroscopy method that removes restrictions on spectral resolution and spectral accuracy in Fourier transform spectroscopy for observing a cyclic repeating phenomenon, that realizes, theoretically, infinitesimal spectral resolution accuracy. After accurately and sufficiently stabilizing the repetition period of a phenomenon, a temporal waveform is acquired by making a repetition period and a time width for observing the temporal waveform of a phenomenon strictly conform, and by performing a Fourier transform, acquired is a discrete separation spectrum in which the inverse number of the observation time window size T is made a frequency data gap. Measurement is repeated while causing the repetition period to change, and the gap of the discrete separation spectrum is supplemented. Thereby, in a case of an observation target in which the existence time of a phenomenon is longer than the repetition period, the spectral resolution of the obtained discrete separation spectrum becomes infinitesimal.