A fast wavelet algorithm on the interval

The Franklin system is an orthonormal basis of L²[0,1]. The authors give a multiresolution analysis of L²[0,1] using the Faber-Schauder system. Exact reconstruction is now allowed; the authors perform a comparison with the Stromberg system (on [0,1]) where an edge error appears when the reconstruction is made. They derive a fast algorithm which enables one to analyze and synthesize a given signal on an interval. When using the Franklin system, it appears that special considerations are held near the edges where the extension of the signal over the edges is no longer needed (zero-padding method...etc.). Numerical simulations are provided to emphasize the performances of the results