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Terahertz time-domain spectroscopy (THz-TDS) based on high-speed asynchronous optical sampling (ASOPS) with two offset-locked GHz femtosecond lasers requires no mechanical time-delay scanner. Consequently, measurements with 1-GHz frequency resolution are performed at intrinsically high scan rates in the multikilohertz range. This is at least one order, in most cases several orders of magnitude faster than conventional approaches employing mechanical time-delay scanners. We report a system offering a unique combination of high-frequency resolution (1 GHz) and high scan rate (2 kHz) with a spectral coverage of more than 6 THz. Its capabilities for high-precision spectroscopy are demonstrated by measuring the absorption spectrum of a mixture of \H2\O, D_2O, and hydrogen deuterium oxide (HDO) vapor. \H2\O and HDO vapor absorption spectra are accurately tabulated in databases. However, D_2O absorption data are rare, because of residual \H2\O and HDO often present when measuring pure D_2O. Here, we present a high-resolution absorption spectrum of D_2O vapor numerically extracted from the absorption spectrum of the three-component mixture. In addition, we show that the high spectral resolution of the ASOPS THz-TDS system provides benefits in the analysis of frequency-selective surface sensors, which are promising candidates for biosensing applications in the THz regime. [ABSTRACT FROM PUBLISHER]