On the time-frequency analysis of signals that decay exponentially with time

The use of the short-time Fourier transform and the wavelet transform implemented using the new harmonic wavelets for analyzing the time variation of the spectral contents of exponentially time-decaying signals is studied in the present investigation. Focus is also placed on how well these methods can recover the decay constant of each frequency component in the signals in a relatively narrow bandwidth situation. Both artificial and experimentally recorded signals have been used. Results suggest that the short-time Fourier transform is in general more reliable than the wavelet transform for the present purpose. The short-time Fourier transform also gives excellent recovery of the decay constants if the signals are made up of discrete frequency components.