Generalized time-frequency representation of ultrasonic signals

Time-frequency representation of ultrasonic signals plays an important role in describing the scattering and dispersive effects in materials. Cohen´s class of generalized time-frequency representation (GTFR) has been examined for ultrasonic applications. Two special cases of GTFR, Wigner-Ville distribution (WVD) and Choi-William distribution (CWD) are discussed. Due to the bilinear structure, all GTFRs´ generate cross-terms for the multicomponent signals. The presence of cross-terms in the WVD of a multicomponent signal obscures the auto-terms. The cross-terms in CWD can be controlled by choosing a proper scale factor which does not effect the marginals. It is shown that the estimation of local time and frequency of ultrasonic echoes corrupted with noise can be accurately performed using CWD. Short-time Fourier transform (STFT) or spectrogram is also discussed as a class of GTFR. STFT or spectrogram does not satisfy the marginals. Simulated results show that CWD outperforms WVD and STFT because it is not marred by severe interference due to cross-terms, still able to satisfy the marginals, and it provides the best resolution in time-frequency plane