Studies of boundary problem based on wavelet series for a finite interval

Traditional Fourier analysis is applied to signal processing, but it often causes `jump´ at the edges. In this paper, a quantitative analysis of the `jump´ and a wavelet series construction method by folding and integral operator in the H¹[0,1] space are introduced. Its good properties are discussed here for the first time. Without the need of pre-filtering and boundary extension, the proposed method has the most superior non-boundary distortion. The numerical experimental results show that this wavelet series yields higher approximation precision with less calculation. This new series has more advantages relative to Fourier analysis in dealing with boundary problem, and the wavelet analysis theory is further enriched.