Time shifting is an important procedure required in acoustic applications and research such as producing interaural time difference in auralization for audio virtual reality and simulating multiple inputs for spatial sound signals in research on microphone arrays. Traditional analog time-shifting methods necessitated electronic delay lines, which were a burden on hardware. Instead, more recent digital methods performed time shifting using software. However, the digital methods required an extraordinarily high-sampling rate in order to achieve a reasonable precision in time shifting. Most of the digital methods so far employed interpolation to cope with this problem, although interpolation incurred a great amount of extra computation. A high-precision frequency-domain time-shifting method was recently developed for the purpose of digital implementation of broadband beamformers [Liu and Sideman, J. Acoust. Soc. Am. 98, 241--247 (1995)]. In this study, the above method was extended to more general application contexts. The interpolation was employed implicitly in this method. The computation was required only for doing FFT and unrelated with interpolation. Theoretically, the time-shifting precision can be arbitrarily high whereas the amount of computation was kept constant. Moreover, this method can easily be implemented in real time by means of the conventional short-term Fourier transform.