Recovery of transit times and frequencies of multiple pulses via the Short-Time Fourier Transform

Abstract

In this work, we present a study to determine the transit times and frequencies of pulses by usingthe Short-Time Fourier Transform (STFT). We consider the case of an acoustic signal composed offive Gaussian pulses which have a high overlapping in time but oscillate at different frequencies. Weproceeded in three steps. First, we illustrate how the STFT calculated through a sliding windowproduces a spectrogram where transit time is on one axis and frequency on the other. Second, wederive an exact analytical solution of the STFT to develop an intuitive vision of the mathematicaltechnique. Finally, in a third step, we present an experiment to demonstrate that the STFT is auseful technique to characterize a complex acoustical signal.