Design of optimal FIR prefilters for wavelet coefficient computation

M.J. Shensa previously proposed an algorithm in the computation of wavelet series transform (WST) or continuous wavelet transform (CWT), where a sampled signal is first prefiltered. The Mallat´s discrete wavelet transform (DWT) algorithm is then applied to the prefiltered sequence. The prefiltering is used to reduce the approximation error between the computed and desired wavelet transform coefficients. The optimal finite impulse response (FIR) prefilter design problem for the Shensa algorithm in computing the WST coefficients is studied. It is shown numerically that the error for the computed WST coefficients is reduced significantly more by using the designed optimal prefilters than that obtained from the algorithm of S. Mallat