Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Perfect Reconstruction Conditions and Design of Oversampled DFT-Modulated Transmultiplexers | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID 15756 Pages 1-14 DOI ASP 2006 15756 Perfect Reconstruction Conditions and Design of Oversampled DFT-Modulated Transmultiplexers Cyrille Siclet 1 Pierre Siohan 2 and Didier Pinchon3 1 Laboratoire des Images et des Signaux LIS Universite Joseph Fourier 38402 Saint Martin d Heres Cedex France 2 Laboratoire RESA BWA Division Recherche et Développement France Telecom 4 rue du Clos Courtel 35512 Cesson Sévigné Cedex France 3 Laboratoire Mathematiques pour l Industrie et la Physique MIP Universite Paul Sabatier Toulouse 3 31062 Toulouse Cedex9 France Received 1 September 2004 Revised 12 July 2005 Accepted 19 July 2005 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. Copyright 2006 Cyrille Siclet et al. This is an open access article .
