Open Access

Perfect Reconstruction Conditions and Design of Oversampled DFT-Modulated Transmultiplexers

  • Cyrille Siclet1,
  • Pierre Siohan2 and
  • Didier Pinchon3
EURASIP Journal on Advances in Signal Processing20062006:015756

https://doi.org/10.1155/ASP/2006/15756

Received: 1 September 2004

Accepted: 19 July 2005

Published: 29 March 2006

Abstract

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.

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Authors’ Affiliations

(1)
Laboratoire des Images et des Signaux (LIS), Université Joseph Fourier
(2)
Laboratoire RESA/BWA, Division Recherche et Développement, France Télécom
(3)
Laboratoire Mathématiques pour l'Industrie et la Physique (MIP), Université Paul Sabatier

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Copyright

© 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.