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Calcul cablé d'une transformée de Fourier à très grand nombre d'échantillons, éventuellement multi-dimensionnelle

Abstract : The hard-wired computation of a Fourier transform allows to increase its computation speed. Military applications have used such solutions, with a low number of samples and low accuracy. Pushing away these barriers needs decreasing the area of implementation. A large number of butterflies, cells of calculation, implementing serial operators and working simultaneously allows to obtain a better accuracy and a higher speed. The overcost in term of area has been studied through an implemantation that is presented with its prospects. A multichip solution imposes the choice of a two-level architecture, serial butterflies and parallel communication buses, one is favoured in term of working ratio and frequency. The accuracy is a function of that of original data and of number of steps, then of number of samples. Operators with a variable size allow to favour accuracy and area or speed, according to the number of rows of butterflies. The parameters of operators optimize the architecture of a Fourier transform for a given decimation. 2 and 4 radices only are really used for decimation at the level of computation. The estimate of area and computation time demonstrates winnings for hard-wired solutions for 8 and 12 radices. Multidimensional transforms show a lower phenomenon of error, for a given total number of samples, because of a larger number of simple exponential coefficients. These are the target of civil applications for a large number of samples, images or spatial data. The crystallographic method is one of them, besides with the presence of many samples having a null value. That leads to study the error in the case of sparse matrices, in sight of using existing chips beyond their original applications. These different ways allow to contemplante implementing hard-wired architectures for Fourier transforms with a large number of samples, particularly in case of multidimensional transforms.
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Submitted on : Wednesday, October 26, 2005 - 8:46:32 AM
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A. Vacher. Calcul cablé d'une transformée de Fourier à très grand nombre d'échantillons, éventuellement multi-dimensionnelle. Micro et nanotechnologies/Microélectronique. Institut National Polytechnique de Grenoble - INPG, 1997. Français. ⟨tel-00010763⟩

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