Short-time Fourier transforms (STFT) are useful for analyzing signals with harmonics that vary with time. If the variation of the harmonics with time is smooth, such as in kinematic vibrations in vehicles, then it is possible to improve the STFT using order spectra and correlation analysis. In this paper, it is shown how correlation analysis can be performed when the speed signal is noisy or unknown and then it is shown how order spectra become simple to compute after this analysis. The results are illustrated by an analysis of axle and car body vibrations in the prototype high-speed train, HSR-350x.