A general analysis of cyclic block transmultiplexers with cyclic convolution

In this paper we investigate the class of cyclic block transmultiplexers (TMUXs). The perfect reconstruction (PR) conditions of their prototype function are derived both in time and frequency domain. A duality theorem is provided showing the connection between each PR solution in the frequency domain with its dual in time domain. Then, introducing a decomposition theorem, we obtain fast TMUX implementations. In a particular TMUX setting, we also propose an implementation scheme that only involves independent angular parameters.