Abstract:

The paper uses the characteristics of wavelet multiresolution to decompose singularity signals , and locates the singularity positions of singularity    signals using the decomposed signals. The Lipschitz index is used to describe the function singularity quantitatively. When the wavelet transform scale    becomes tinier and tinier, the maximum signal singularity points＇ attenuation speed of the wavelet transform modulus depends on the Lipschitz index of   the relevant singularity point. Wavelet transform can not only decide the generation time of the singularity point, but also judge the singularity prop erty further.

Key words: wavelet transform;singularity;Fourier transform;multiresolutlon analysis