We show theoretically and experimentally that accurate transport measurements are possible even within the short time provided by pulsed magnetic fields. For this purpose, a new method has been devised, which removes the noise component of a specific frequency from the signal by taking a linear combination of the results of numerical phase detection using multiple integer periods. We also established a method to unambiguously determine the phase rotation angle in AC transport measurements using a frequency range of tens of kilohertz. We revealed that the dominant noise in low-frequency transport measurements in pulsed magnetic fields is the electromagnetic induction caused by mechanical vibrations of wire loops in inhomogeneous magnetic fields. These results strongly suggest that accurate transport measurements in short-pulsed magnets are possible when mechanical vibrations are well suppressed.