The Stromberg wavelet and the Franklin system

摘要

The Franklin (1928) system is an orthonormal basis of L/sup 2/(0, 1). The authors give a multiresolution analysis of L/sup 2/(0, 1) and study the reconstruction error made when the Stromberg (see Proc. 21 Nordic Conf. Math., June 1992) analysis (on (0, 1)) is performed instead of the Franklin one. They derive a fast algorithm which enables one to analyze and synthesize a given signal on an interval. Special considerations are held near the edges where the extension of the interval is no longer needed (zero-padding method, etc.). Numerical simulations are provided to emphasize the performances of their results.