Abstract:

The purpose of this paper is to overcome the boundary trouble when the function in a bounded interval is expanded to wavelets.First,the necessary and suficient conditions of constructing the M-band band-limited scaling function aye presented.Next,by the orthogonal muhiresolution analysis,the necessary conditions of a kind of Mband band-limited orthogonal wavelet function constructed by the scaling function are proposed. By means of weighed orthogonal polynomials and the wavelet functions,the M-band band-limited orthogonal wavelet-like functions in a bounded interval are then established.By the above mentioned methods,the functions in a bounded intenral can be expanded as the sum of finite tems of the scaling functions and wavelet.like functions,thus the nu-merical analysis of partial diferential equations,the regression function estimation and the signal processes can be easily deah with.

Key words: band limiting, M-band orthogonal wavelet bases, M-band multiresolution analysis, scaling function