Effectiveness of the continuous wavelet transform in the analysis of some dispersive elastic waves

Abstract

Although there have been many investigations employing the continuous wavelet transform for the analysis of dispersive waves, they seem to lack theoretical justifications for the effectiveness of the continuous wavelet transform (CWT) over other time–frequency analysis tools such as the short-time Fourier transform (STFT). The goal in this paper is to offer theoretical and experimental justifications for its effectiveness by comparing the performance of CWT and STFT in terms of their time–frequency analysis capabilities of certain dispersive elastic waves. The waves in consideration are elastic flexural waves generated by an impact in a solid circular cylinder. The ridge analysis procedure is employed to estimate instantaneous frequencies by CWT and STFT. Although in the present investigation we are focused on a limited class of dispersive waves, it gives an insight into the effectiveness of CWT for the analysis of other types of dispersive wave systems.