An algebraic construction of orthonormal M-band wavelets with perfect reconstruction

This paper presents an algebraic approach to construct M-band orthonormal wavelet bases with perfect reconstruction. We first derive the system of constraint equations of M-band filter banks, and then an algebraic solution based on matrix decomposition is developed. The structure of the solutions is presented, and practical construction procedures are given. By using this algebraic approach, some well-known K-regular M-band filter banks are constructed. The advantage of our approach is that more flexibility can be achieved, and hence we can select the best wavelet bases for a general purpose or a particular application.