  Fourier transform spectroscopy (FTS) has been widely used in a variety of
fields in research, industry, and medicine due to its high signal-to-noise
ratio, simultaneous acquisition of signals in a broad spectrum, and versatility
for different radiation sources. Further improvement of the spectroscopic
performance will widen its scope of applications. Here, we demonstrate improved
spectral resolution by overcoming the time window limitation using discrete
Fourier transform spectroscopy (dFTS) with precisely periodic pulsed terahertz
(THz) radiation. Since infinitesimal resolution can be achieved at periodically
discrete frequencies when the time window size is exactly matched to the
repetition period T, a combination of THz-dFTS with a spectral interleaving
technique achieves a spectral resolution only limited by the spectral
interleaving interval. Linewidths narrower than 1/(50T) are fully resolved
allowing the attribution of rotational-transition absorption lines of
low-pressure molecular gases within a 1.25 MHz band. The proposed method
represents a powerful tool to improve spectrometer performance and accelerate
the practical use of various types of FTS.
