In this study, the recently-proposed adaptive wavelet transform (AWT) and synchro-squeezed adaptive wavelet transform (SSAWT) are introduced with their optimum transformation parameters automatically searched to derive at a desirable time-frequency representation of any dynamic response. The AWT enables the selectivity of time and frequency resolution in a domain of interest and the synchro-squeezing algorithm reduces the dispersion of a scalogram of the AWT, facilitating an accurate extraction of frequency features over time. The effectiveness of AWT is first demonstrated with an illustrative signal of four time segments covering various frequency distribution cases. In comparison with conventional wavelet transform, the AWT can clearly separate time-varying frequency features from the signal. Accordingly, the SSAWT is at least 5 times more accurate with a 1.1% error than conventional synchro-squeezed wavelet transform. The AWT is then applied to the impact echo (IE) responses experimentally recorded from a 60"×36"×7.25" concrete slab for potential pavement applications. The time-frequency resolution and corresponding frequency spectra led to the successful detections of deep pavement defect, shallow pavement defect or no pavement defect from 40 sets of experimental data. The SSAWT results in a 1.5% estimation error in the identification of deep pavement defect depth and a 5% estimation error in slab thickness, both being twice more accurate than the AWT in terms of estimation error. The selection process of time-varying central frequencies, scaling factors, and window lengths proves robust.