Didier Pinchon

Design techniques for orthogonal Modulated filterbanks based on a compact representation

This paper presents a method to design perfect reconstruction orthogonal modulated filterbanks having a very large number of subbands. At first, using the angular parameterization of the underlying lattice structure, the problem is formulated as an unconstrained optimization problem. Then, it is shown for two different optimization criteria (the minimization of the out-of-band energy and the maximization of the time-frequency localization) that the optimized lattice coefficients can be interpolated in two different ways. A first characterization takes advantage of the fact that the angles related to successive polyphase components of the prototype filter have a smooth behavior. A new parameterization, named compact representation, is therefore introduced, which shows that a linear increase of the number of parameters with respect to the number of subbands can be avoided with practically no loss of accuracy. A second observation concerns the also smooth behavior of each angular parameter when considering an increasing number of subbands. The efficiency of the two approaches is illustrated by the design of filterbanks with a large number of subbands going from 32 up to 4096, including prototype filters up to a length of 32 768.

Analysis, design, and implementation of two-channel linear-phase filter banks: a new approach

The problem of designing two-channel perfect-reconstruction FIR filter banks with linear-phase analysis and synthesis filters is revisited. Based on a new algebraic formulation, all the possible factorized forms for this two-band filter bank are derived. We thus obtain complete and canonical solutions for the filter banks, composed of odd-order symmetric and antisymmetric filters (type-A systems) and for those built with symmetric even order filters (type-B systems). A strong characteristic of these new cascade structures, which, until now, had not been identified, is related to a defectivity property. Taking this into account is the key issue to cover all the FIR solutions and to design cascade structures being robust to the quantization of their parameters. Design examples are provided that illustrate our method.

On the area swept under the occupation process of an M/M/1 queue in a busy period

AbstractWe compute in this paper the distribution of the area

A fast design method for orthogonal modulated filter banks

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On a random variable associated with excursions in an M/M/\infty system

swept under the occupation process of an M/M/1 queue during a busy period. For this purpose, we use the expression of the Laplace transform

A Design Technique for Oversampled Modulated Filter Banks and OFDM/QAM Modulations

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