Wavelet transform signal processing for dispersion analysis of ultrasonic signals

The wavelet transform provides a new tool for analyzing the time-frequency evolution of transient signals as an alternative to the classical short-time Fourier transform. The purpose of the present paper is to provide an overview of the applicability of the wavelet transform technique to the analysis of the propagation of dispersive ultrasonic waves. The wavelet transform is briefly introduced, with special emphasis on the relationship between the wavelet transform and the group velocity of dispersed signals. A complex mother wavelet is utilized to obtain the time evolution of the various spectral components of the ultrasonic signal, and the magnitude of the wavelet transform is used to represent the envelope of the ultrasonic pulse and to determine the time of arrival of the acoustic energy. This approach results in a time-scale representation of the ultrasonic signal which is extremely useful in the characterization of thin coatings using the dispersion behavior of the surface wave velocity. The technique was applied for the measurement of elastic constants of chromium coatings on steel substrates using laser-generated surface acoustic waves. Numerical simulations and experimental results are presented to discuss the usefulness of the wavelet transform.