Leonard F.

The short-time Fourier transform (STFT) yields a complex distribution function which cannot be used directly for illustration in the time-frequency plane. Until recently, the results of STFT calculations have always been presented in the form of a power spectrogram where only the amplitude value of the STFT is shown. The problem is that the phase information is only partially included and furthermore is mixed with amplitude information, which means that we are deprived of an important source of information. The aim of this paper is to present two different ways of using the STFT phase information. The frequency spectrogram is calculated from the phase difference between each time slice of the STFT. The frequency spectrogram shows the drift on the instantaneous frequency of each spectral component. Time integral of the frequency spectrogram yields the phase spectrogram. The phase spectrogram supplies information about the phase modulations of each spectral component around a reference time point. These tools have proven to be useful complements to the power spectrogram. Digital simulations together with examples from measurements of mechanical vibrations bear witness to the usefulness and accuracy of these new tools.