Time-reversed inversion for time-varying filter banks

For an analysis/synthesis filter bank to achieve perfect reconstruction, the synthesis polyphase matrix should be equal to an inverse of the analysis polyphase matrix E(z). Therefore, the problem of perfect reconstruction filter banks is same as the inversion of the multi-input multi-output transfer function E(z). Using state-space notations, it has been shown that the inversion can be achieved by using time-reversed filters given proper initial conditions. In this paper, we extend the idea of time-reversed inversion to the case of time-varying filter banks. Using the state-space framework, we show perfect reconstruction is always guaranteed, no matter how often the filter bank varies with time. This framework covers both maximally-decimated filter banks and under-decimated ones. We also show how the overhead of transmitting initial conditions can be avoided