Perfect Reconstruction Conditions and Design of Oversampled DFT-Modulated Transmultiplexers

  • Cyrille Siclet
  • Pierre Siohan
  • Didier Pinchon
Open Access
Research Article
Part of the following topical collections:
  1. Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory


This paper presents a theoretical analysis of oversampled complex modulated transmultiplexers. The perfect reconstruction (PR) conditions are established in the polyphase domain for a pair of biorthogonal prototype filters. A decomposition theorem is proposed that allows it to split the initial system of PR equations, that can be huge, into small independent subsystems of equations. In the orthogonal case, it is shown that these subsystems can be solved thanks to an appropriate angular parametrization. This parametrization is efficiently exploited afterwards, using the compact representation we recently introduced for critically decimated modulated filter banks. Two design criteria, the out-of-band energy minimization and the time-frequency localization maximization, are examined. It is shown, with various design examples, that this approach allows the design of oversampled modulated transmultiplexers, or filter banks with a thousand carriers, or subbands, for rational oversampling ratios corresponding to low redundancies. Some simulation results, obtained for a transmission over a flat fading channel, also show that, compared to the conventional OFDM, these designs may reduce the mean square error.


Quantum Information Fading Channel Design Criterion Filter Bank Initial System 


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Copyright information

© Cyrille Siclet et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Cyrille Siclet
    • 1
  • Pierre Siohan
    • 2
  • Didier Pinchon
    • 3
  1. 1.Laboratoire des Images et des Signaux (LIS)Université Joseph FourierSaint Martin d'Hères CedexFrance
  2. 2.Laboratoire RESA/BWA, Division Recherche et DéveloppementFrance TélécomCesson Sévigné CedexFrance
  3. 3.Laboratoire Mathématiques pour l'Industrie et la Physique (MIP)Université Paul SabatierToulouse Cedex 9France

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