Abstract: In this paper, Wavelet transform is used to analyze the singularity of a given signal. Based on the method of wavelet transform mudulus maxima (WTMM), the characters of fractal set of triadic Cantor is studied. It is shown that one can, not only determine the singular position of signal, but also estimate the Holder exponent h which describes the strength of singularity and other parameters correctly. In addition, the temperature data in Rayleigh-Benard convection is studied using the above procedures. It is observed that the temperature data exhibit multi-fractal hierarchy and multi-scale structures. The obtained results agree well with those determined from the viewpoint of fractal measures.