Quasi positive sampling in wavelet subspaces

The wavelet transform is an innovative tool for function approximation and signal compression. It has some advantages in the analysis of signals compared to other orthogonal systems. However, as with other classical orthogonal systems, it presents problems as excessive oscillations in the partial sums and the Gibbs phenomenon can arise S. E. Kelly (1996). In other orthogonal systems this problem is solved using summability methods but these methods cannot be implemented as they are in wavelet expansions. Walter and Shen (1998), propose an alternative method for wavelet systems. However, its practical implementation presents computational problems. This paper considers a modification of Walter and Shen (1998), for approximation of signals hi the interval [0, ∞] where, through the truncation of sums, we obtain a better computational behavior.