Theory and design of perfect reconstruction transmultiplexers and their relation to perfect reconstruction QMF banks

Abstract

The theory of transmultiplexers involves the design of filters for interconversion between Time Domain Multiplexing (TDM) and Frequency Division Multiplexing (FDM), such that the undesirable Crosstalk is minimized. In TDM → FDM → TDM conversion, the perfect reconstruction trans-multiplexer (PR-TMUX) achieves complete Crosstalk Cancellation (CC) and is distortion-free. In this paper, we present an analysis of the PR-TMUX based on the polyphase component matrices of the filter banks used in TDM → FDM and FDM → TDM conversion respectively. Using that, a necessary and sufficient condition for complete CC is obtained. The close relation between PR-TMUX filters and PR-QMF banks is used to obtain a direct design procedure for PR-TMUX filters.

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