Parameter estimation for wavelet transformed ultrasonic signals

In this paper, we first present a closed-form analytical solution for Wavelet transformed ultrasonic signals, which can be utilized for non-destructive evaluation. A family of wavelet transformed multiple echo ultrasonic signals is parameterized in terms of the closed-form solutions. For the given noisy version of wavelet transformed multiple echoes, the separable nonlinear least squares (SNLS) technique is applied to estimate the associated unknown parameters. For an illustrated example, the Cramer–Rao lower bound (CRLB) of the covariance matrix of the estimated parameters is calculated and compared to the covariance matrix generated by Monte Carlo simulations. The proposed method is applied to two illustrative examples and to actual ultrasonic A-scan data from water-immersion tests to demonstrate its usefulness as an effective non-destructive evaluation technique.