A general overview of cyclic transmultiplexers with cyclic modulation: Implementation and angular parametrization.

Didier Pinchon (1) , Pierre Siohan (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Orange Labs, 35512 Cesson-Sévigné, France

This preprint provides a general framework for cyclic transmultiplexers (TMUXs) with cyclic modulation. This TMUX also corresponds to a multicarrier modulation system of the Filtered MultiTone (FMT) type where the linear convolution is replaced by a cyclic one, hence the name Cyclic Block FMT (CB-FMT). In this preprint we present the Perfect Reconstruction (PR) conditions in the time and frequency domains. A duality theorem is proved showing that each PR solution in the frequency domain is connected to a dual PR solution in the time domain. Then, two decomposition theorems are established leading to modular implementations of the cyclic TMUX. For one of this implementation we provide an angular parametrization that only involves angles corresponding to independent parameters. Finally, a procedure to reconstruct the prototype function from all the elementary blocks of the modular implementation is described step-by step.

Mots clés: Cyclic transmultiplexer; cyclic modulation; perfect reconstruction; angular parametrization

Domaines: Mathématiques générales [math.GM]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Didier Pinchon, Pierre Siohan. A general overview of cyclic transmultiplexers with cyclic modulation: Implementation and angular parametrization.. 2014. ⟨hal-01011408⟩