Integer- and rational-coefficient M-band wavelet

This paper introduces a family of symmetric biorthogonal M-band wavelets with rational and integer coefficients and up to 2 degrees of regularity. Unlike previous approaches, we construct M-band wavelets by adding simple pre/post-filtering modules along the block boundaries of the traditional block DCT framework. Integer- and rational-coefficient solutions are then obtained from placing further restrictions on each involved component. In other words, we address the design and implementation of fast, efficient pre/post-filters that help improve the polynomial-representing and capturing capability of traditional block transforms such as the DCT. Fast symmetric integer-mapping M-band wavelets can be easily generated by iterating our decomposition scheme on the lowpass subband. Several design examples are presented to demonstrate the validity of the proposed theory.