Gabor transform with optimal time-frequency resolution for ultrasonic applications

The resolution of a t-f distribution is important for flaw detection and characterization in ultrasonic nondestructive evaluation. Wigner-Ville distribution (WVD) exhibits the true t-f resolution of an ultrasonic echo on a joint t-f plane. But this important characteristic of WVD is of no use for multiple ultrasonic echoes due to inherent cross-term artifacts. An alternative to WVD is Gabor Transform (GT), a signal decomposition method, which displays the time-frequency energy of a signal on a joint t-f plane without generating cross-terms. This desirable characteristic is achieved at the expanse of t-f resolution. In this study we are performing both analytical and numerical evaluation of GT t-f resolution for ultrasonic applications. We have generated a set of curves from the analytical solution that depict t-f resolution (concentration) of a Gaussian ultrasonic echo for different values of GT window duration. With the a priori knowledge of measurement system's characteristics we can choose an optimal GT window parameter for better detection of multiple echoes in both time and frequency. We present examples that demonstrate performance of GT with optimal resolution in comparison to WVD. In addition experimental results will be provided that demonstrate improved detection and characterization of multiple ultrasonic echoes.