Implementation and perfect reconstruction of a maximally decimated FIR filter bank using parallel module decomposition

This paper discusses an implementation and the perfect reconstruction (PR) of an M-channel maximally decimated FIR fitter bank. Using the polynomial module arithmetics, the filter bank is decomposed into a set of module filter banks of size M, independent of the filter length. When the filter bank is uniform, the computational cost is the same as the polyphase/FFT implementation. When it is not uniform, in which case the polyphase/FFT implementation is not applicable, the computational cost is still reduced by sharing among channel filtering computations. The parallel module configuration is favorable for hardware implementation because decomposing a large system into small subsystems is generally advantageous for many realizations. The PR analysis is greatly simplified by working on the module filter banks as well