Gabor coefficients for estimation of arrival time and center frequency of ultrasonic echoes

Detection of defects in complex materials which may result in multiple and dispersive interfering echoes is an important task in ultrasonic nondestructive evaluation (NDE). Materials can be effectively characterized and defects can be localized by estimating arrival times, and frequency bands of ultrasonic backscattered echoes. In this paper we present Gabor coefficients (Discrete Gabor representation) as a method of a linear time-frequency representation. The Gabor coefficients detect multiple defect echoes with unknown times of arrival and center frequencies by displaying them on a joint time-frequency plane. The Gabor coefficients are calculated via Zak transform, an efficient method, because it utilizes the fast Fourier transform. It has been observed that Gabor coefficients estimated via Zak transform are robust and discern multiple ultrasonic echoes overlapped partially or totally both in time and frequency under a very low SNR environment, where the ratio of peak echo to peak noise is approximately 0 dB. Therefore, the Gabor coefficients representation is an effective tool for characterizing and localizing of multiple defects in the nondestructive evaluation of materials.