THE THEORY AND DESIGN OF ARBITRARY-LENGTH COSINE-MODULATED FILTER BANKS AND WAVELETS, SATISFYING PERFECT RECONSTRUCTION

It is well known that FIR filter banks that satisfy the perfect-recons truction (PR) property can be obtained by cosine modulation of a linea r-phase prototype filter of length N = 2 nM, where M is the number of channels, In this paper, we present a PR cosine-modulated filter bank where the length of the prototype filter is arbitrary, The design is f ormulated as a quadratic-constrained least-squares optimization proble m, where the optimized parameters are the prototype filter coefficient s. Additional regularity conditions are imposed on the filter bank to obtain the cosine-modulated orthonormal bases off compactly supported wavelets. Design examples are given.