Wavelet coefficient computation with optimal prefiltering

From the derivations given in Section 11, the polynomial residue number system can be interpreted by the terminology of Chinese remainder theorem for polynomials over a finite ring, which is more familiar for the computer and signal processing societies. Abstract-Discrete wavelet transform (DWT) is often used to approximate wavelet series transform (WST) and continuous wavelet transform (CWT), since it can be computed numerically. In this research, we first study the accuracy of the computed DWT coefficients obtained from the Shensa algorithm as an approximate of the WST coefficients. Based on the accuracy analysis, we then propose a procedure to design optimal FIR premters used in the Shensa algorithm to reduce the approximation error. Finally, numerical examples are presented to demonstrate the performance of the optimal FIR preMters.