On optimal prefiltering for wavelet coefficient computation

The authors use an algorithm proposed by M.J. Shensa (1992) for computing the coefficients of the wavelet series transform (WST) or continuous wavelet transform (CWT) to filter a sampled discrete-time signal and then apply S. Mallat´s (1989) discrete wavelet transform (DWT) algorithm to the filtered sequence. The prefiltering is used to reduce the approximation error between the computed and desired coefficients. The design of optimal causal and noncausal FIR prefilters which reduce the approximation error as much as possible is considered. Numerical experiments are provided to demonstrate the performance of these optimal prefilters