Fast algorithm of wavelet decomposition and reconstruction for the fractal signals

A fast algorithm of wavelet decomposition and reconstruction for fractal signals is put forward. In accordance with the self-similarity and long-term-related characteristics of the fractal signals, and by means of the discrete wavelet transformation (DWT), multi-scale resolution is carried out so as to make them become similar stationary signals and estimate them with the usual Wiener filtering or Kalman filtering methods. Then multi-scale reconstruction is carried out with DWT in order to estimate the primary signals polluted by noise. This paper stresses the algorithm design of the DWT filtering process, and the computing complexity is also considered