This study examines rationale of correction factor β in the formula of thickness resonant frequency, fundamental to the thickness estimation of impact-echo (IE) approach in nondestructive testing (NDT) for integrity appraisal and damage diagnosis of infrastructure systems. It shows the role of the factor in the formula from the perspective of testing equipment setup, wave propagation, and resonant frequency identification, much broader than what was first introduced empirically for shape correction of a structure under test. Emphasis is laid in wave-based interpretation of resonant frequency, typically obtained from traditional fast Fourier transform (FFT) data analysis of IE recordings. Since the FFT data analysis provides average, not true, characteristic of resonant frequency shown in the nonstationary IE recordings, it typically distorts the thickness estimation from the formula if the correction factor is not used. An adaptive time-frequency data analysis termed Hilbert–Huang transform (HHT) is then introduced to overcome the shortage of FFT analysis in identifying the resonant frequency from noise-added IE recordings. With FFT and HHT analyses of five data sets of sample IE recordings from sound and damaged concrete structures and comparison with referenced ones, this study reveals that the proposed IE approach with HHT data analysis not only eliminates the subjective use of correction factor in the formula, but it also improves greatly the accuracy in the thickness estimation.