Statistical behavior of wavelet transmultiplexers in arbitrary synchronization states

Wavelet transmultiplexers based on orthogonal perfect reconstruction filter banks can play a role in channel encoding for digital communications. Synchronization of the receive end of the transmultiplexer is needed for reliable communication, imposing certain requirements for acquisition and tracking. Consequently, the response of the transmultiplexer in out-of-synchronization states is of interest in developing ways to acquire and track. We prove that a two-band, J-stage wavelet transmultiplexer based on a perfect reconstructing, orthonormal filter bank maps stationary, uncorrelated white input processes into stationary, zero-mean, uncorrelated white output processes, independent of the synchronization state.