Echo Extraction from an Ultrasonic Signal Using Continuous Wavelet Transform
Wavelet transform has already been shown as a useful tool for the interpretation and the enhancement of ultrasonic data in the context of nondestructive evaluation [1–3]. Main applications of the wavelet transform are signal analysis in the time-frequency domain, data compression and now signal processing. Comparisons with other time-frequency representations like short time Fourier transform  and Wigner-ville transform  have shown the usefulness of the continuous wavelet transform for signal analysis: this method is well adapted to localize in time both high and low frequencies and does not introduce interference terms. Another important property is that signal reconstruction can be achieved from wavelet decomposition. This ability allows one to do signal processing in the time-frequency plane. Earlier work has shown the possibilities to use the wavelet transform as a filter for signal-to-noise ratio enhancement  by reconstructing the signal after applying energy thresholding in the time-frequency domain. This reconstruction does not involve global averaging in time or frequency domain because of the good localization of the wavelet coefficients in both domains.
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