In many applications, material parameters are extracted by comparing theoretical models of ultrasonic propagation with experimental measurements. A particular challenge arises in the case of thin materials, for which the ultrasonic signal is dispersive and multiple propagation modes are commonly present. The purpose of this paper is to provide an overview of the applicability of the analytic wavelet transform technique to the analysis of the propagation of dispersive ultrasonic waves. Ridges in the modulus of the transform determine regions in the time and frequency domain with high concentrations of acoustic energy; hence they are the natural candidates for the characterization and reconstruction of the ultrasonic signal. This approach results in a time-frequency representation of the ultrasonic signal that is extremely useful in the characterization of thin coatings or thin plates. The fundamentals and experimental results are presented to show the usefulness of the proposed technique.