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Nonlinear function generation using oversampled Sigma-Delta-modulators

: Machul, O.; Hammerschmidt, D.; Weiler, D.; Hosticka, B.J.

Vandevalle, J.; Gielen, G.:
International Symposium on Circuits and Systems. ISCAS 2000. Proceedings : May 28 - 31, 2000, Geneva, Switzerland
Piscataway, NJ: IEEE, 2000
ISBN: 0-7803-5485-0
S.I/611-I/614 : Lit.
International Symposium on Circuits and Systems (ISCAS) <33, 2000, Geneva>
Fraunhofer IMS ()
Nichtlinearität; Näherungsverfahren; Interpolation; Analog-Digital-Umsetzung

In this paper we present a technique for nonlinear function generation which uses a novel sparse look-up table approach. This novel approach can be derived from the simple look-up table concept and utilizes the interpolating properties of oversampled Sigma-Delta-modulators. We show that the approximation process with oversampled Sigma-Delta-modulators can be generally understood as a weighted sum of piecewise-continuous polynomial B-splines. The weights are digitally stored in a sparse look-up table memory which can be used for the nonlinear function mapping. The shape of the polynomial B-splines depends on the order of the loop-filter which is used in the Sigma-Delta-modulator topology. Detailed investigations of approximation behaviour show that a spectrum of linear, square, and cubic piecewise-continuous interpolation can be achieved if we use up to 3rd order Sigma-Delta-modulators. With the increased order of modulator topology the approximation quality is also improved under the assumption that we use the same weight set for function mapping. The fact that polynomial B-splines delivers only nonzero values within a limited range of input arguments makes this approximation method much less sensitive to local errors than classical approximation methods like Lagrange or Newton interpolation.