Wavelet Analysis And Its Applications To The Detection Of Arriving Points Of Transient Signal And Denoising

This thesis mainly studies the applications of wavelet transform and wavelet packet transform to the transient signal arriving points and transient signal denoising. The major works can be summarized as follows:This thesis studies first the detection of the arriving points of smoothing transient signal. We study carefully the properties of the continuous wavelet transform using Gaussian wavelet and a new method by using the established detection function is proposed to detect the arriving points, and the detection experiments on the signals show the effectiveness of the method.Based on the principle of modulus maximum, a new approach using scalogram of wavelet transform for transient signal, under noise free condition or noise condition separately, is described. The detection is based on the detection of the peaks of scalogram. The scalograms of three kinds of wavelet transforms and selection of parameters are simulated. The result shows that this approach has good detection effect even under low SNR condition and parameters are selected. Compared with the detecting by using wavelet only, this scheme has better adapting ability and detecting ability.According to the excellent time-frequency localization analysis properties of the wavelet packet, this thesis describes the distribution of the transient signal quantitatively in time-frequency space by introducing the cxD -norm. Then proposes a method of noise cancelling and spectral analysis of transient signal. Compared with the Donoho soft-threshold method, the SNR is further increased. Theoretical analysis and the results of experiments both indicate that this method is simple and reliable.