This study examines rationale of correction factor β in the formula of thickness resonant frequency, fundamental to the impact-echo (IE) approach in non-destructive testing and evaluation for integrity appraisal and damage diagnosis of infrastructure systems. It shows the role of the factor in the resonant frequency which is typically obtained with average characteristic from traditional fast Fourier transform or FFT data analysis of IE recordings. A time-frequency data analysis termed Hilbert-Huang Transform or HHT is then introduced to overcome the shortage of FFT analysis in identifying the resonant frequency from IE recordings. With the 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 use of correction factor in the formula, it also improves greatly the accuracy in the IE approach.