2-Norm Based Recursive Design of Transmultiplexers with Designable Filter Length

In this paper, motivated by the facts that shorter length filters offer considerable improvements in computation and hardware implementation and that designable filter length brings more design flexibility, we propose a novel transmultiplexer design method that can not only achieve close-to-perfect reconstruction but also obtain designable filter length. The proposed method is based on a composite distortion measure: the 2-norm of the error transfer matrix of the transmultiplexer. Central to the development is providing an efficient means to recursively design the filters in the transmultiplexer and evaluating the composite distortion measure, which greatly improves the computation efficiency. The simulation results show the effectiveness of the proposed algorithms.