A programmable look-up table-based interpolator with nonuniform sampling scheme

Authors:
Élvio Carlos Dutra e Silva Júnior;Leandro Soares Indrusiak;Weiler Alves Finamore;Manfred Glesner
Affiliations:
Department of Aerospace Science and Technology, Institute for Advanced Studies, Brazil;Department of Computer Science, University of York, York, UK;Department of Eletrical Energy, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil;Department of Microelectronic Systems, Darmstadt University of Technology, Darmstadt, Germany
Venue:
International Journal of Reconfigurable Computing
Year:
2012

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Abstract

Interpolation is a useful technique for storage of complex functions on limited memory space: some few sampling values are stored on amemory bank, and the function values in between are calculated by interpolation. This paper presents a programmable Look-Up Table-based interpolator, which uses a reconfigurable nonuniform sampling scheme: the sampled points are not uniformly spaced. Their distribution can also be reconfigured to minimize the approximation error on specific portions of the interpolated function's domain. Switching from one set of configuration parameters to another set, selected on the fly from a variety of precomputed parameters, and using different sampling schemes allow for the interpolation of a plethora of functions, achieving memory saving and minimum approximation error. As a study case, the proposed interpolator was used as the core of a programmable noise generator--output signals drawn from different Probability Density Functions were produced for testing FPGA implementations of chaotic encryption algorithms. As a result of the proposed method, the interpolation of a specific transformation function on a Gaussian noise generator reduced the memory usage to 2.71% when compared to the traditional uniform sampling scheme method, while keeping the approximation error below a threshold equal to 0.000030518.