The Application Of Wavelet Transform To The Detection Of Transient Signal's Arriving Point

This thesis put particular emphasis on the study and application of continuous wavelet transform to the detection of transient signal's arriving points. The main works and contributions in this thesis are as follow.A survey concerned with the wavelet analysis's developing history, current situation of generalized functions and the research background of signal's arriving points is given. Furthermore, in order to make a necessary foundation for further research, the relevant knowledge about wavelet analysis and generalized functions is introduced briefly.Some commonly used methods used for the detection of transient signal's arriving point are introduced briefly. Aimed at the property of transient signal such as the short-time characteristic, energy -concentration and so on, it makes a preliminary exploration to the measurement of transient signal' s parameters.The relation between the singularity detection and the wavelet transform modulus maxima line's theory is on research in this thesis. And then based on the generalized function and distribution theory, it presents two corollaries that are relate to singularity detection and the wavelet transform modulus maxima line (WTMML' s). The physics meaning of these two corollaries is explained by virtual of the generalized functions' weak-convergence theory.There exist some disadvantages such as low measuring resolution and high calculating amount for multi-scale wavelet transform when the noise in signals is higher. By means of the corollaryâ…¡ of 3.5 which stated that carrying on double wavelet transform to the signal would not change the convergence of modulus maxima line when scale comes to zero, this thesis put forward a new measuring method. When noise including in signal is higher, this new method can still keep a goodprecision of measuring.At last, Matlab and Wavelab are adopted to design and simulate the new measuring method mentioned above by this thesis. The experimental result indicates that this new method has relatively high precision of measuring, and can get the good measuring result.