Design of Optimum Wavelet for Noise Suppression and its Application to Ultrasonic Echo Delay Estimation

In this paper an optimum wavelet for denoising applications based on signal to noise ratio (SNR) improvement is designed. The approach is based on searching for a wavelet basis that provides the best non linear approximation of a given signal. It is shown that such a basis will have the best wavelet denoising performance in the sense of signal estimation error. The performance of this method is studied on a few standard test signals and as a practical application, the proposed method is used for denoising and estimating the time difference of arrival (TDOA) of ultrasonic echoes which are widely used in non destructive testing. Simulation results show an improvement of up to 1.2 dB in SNR enhancement for the given test signals comparing with standard wavelets.