The design of tree-structured M-channel filter banks using perfect reconstruction filter blocks

The concept of perfect reconstruction in filter banks is examined using the Smith form of the polyphase matrix. A class of M-channel FIR (finite-impulse response) perfect-reconstruction filter banks is introduced that includes the recently developed lossless filter banks. With the proposed filter banks, the synthesis filters are of the same complexity as the analysis filters. In addition, the synthesis filter bank is easily obtained from the analysis filter bank by inverting a set of M*M constant coefficient matrices. A statistical method for the design of such filter banks is presented. These can be used as building blocks in large tree-structured filter banks where the overall number of channels is any composite integer. An analysis of the computational and storage complexity of such tree structures is given. The results of the analysis are simple formulas for required storage and computation, which helps in the selection of efficient tree structures.<>