Singular Value Decomposition of Wigner Distribution for Time-Frequency Representation of Ultrasonic Echoes

Wigner distribution (WD) is an effective tool for characterizing non-stationary signals where different frequency components arrive at different times. WD was proposed in 1932 by Wigner with applications in quantum mechanics [1]. WD offers high frequency resolution, and satisfies important properties such as marginals and time/frequency shifts. However, in spite of these advantages, WD creates spurious frequency information (cross-terms) when it is applied to signals consisting of multiple echoes or to a signal corrupted by noise. The cross-terms interfere with and often mask the true time-frequency information associated with echoes of interest. Due to the random and complex nature of backscattered ultrasonic echoes, and because the echoes are not exactly Gaussian in shape, the WD of ultrasonic signals is corrupted by the cross-terms. In this paper, singular value decomposition (SVD) is used to analyze and reduce the cross-terms.