To overcome the limitations of spectral resolution and spectral accuracy in Fourier transform spectroscopy to observe the periodic repetition phenomenon, realized on the theory, spectral decomposition of the infinitesimal (the spectral resolution of infinity), improve the spectral accuracy to provide a Fourier transform spectroscopy possible. The repetition period of the phenomenon in terms of an exact and fully stabilized, exactly match a repeating cycle and the time width (observation time window T) to observe the time waveform of the phenomenon to get the time waveform, to Fourier transform by, the inverse of the observation time window T to get a discrete distribution spectrum with a frequency data interval. While changing the repetition period repeat the measurement, to supplement the gap of discrete distribution spectrum. This in case the existence time of the phenomenon is the repetition of a long observation target than the period, the acquired discrete spectral decomposition is infinitesimal of distribution spectrum (spectral resolution is infinite), and can improve the spectral accuracy.
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