| The joint time-frequency (t-f) display of non-stationary backscattered ultrasonic echoes reveals important information to characterize the target echoes in the non-destructive testing of materials. Generalized t-f distribution (e.g., Wigner-Ville distribution, Chow-Williams exponential distribution, etc.) applied to ultrasonic backscattered echoes generates artifacts known as cross-terms. These cross-terms mask the t-f information of the target echoes and make the evaluation of the material difficult. An alternative is Gabor Transform (GT), which displays the joint t-f information without generating cross-terms. However, the fixed window of GT limits its t-f resolution. The signal components with period longer than the window width may be misinterpreted and the time resolution of high frequency signal components is limited due to the finite window width. In this paper we apply a novel t-f method, S-Transform (ST), which uses the t-f representation of GT with a frequency dependent window. We have explored the performance of S-transform as applied to ultrasonic non-destructive testing of materials. ST detects multiple target echoes in both time and frequency without the a-priori knowledge of the measurement system's characteristics. ST, combines the time-frequency representation of the GT and multi-resolution feature of Wavelet Transform (WT), is a unique t-f representation. It adapts the Fourier Transform (FT) in analyzing the localized signal by applying a frequency-dependent time-scaling window. These characteristics make the ST a useful tool to characterize the ultrasonic backscattered target echoes embedded in the microstructure noise for flaw detection in the materials. Simulation results depict correct t-f information of multiple Gaussian Echoes under low SNR environment. In addition, experimental results demonstrate better and reliable detection and characterization of backscattered target echoes in the presence of microstructure noise. |