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Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2

Abstract : We address the problem of synthesizing a generalized Gaussian noise with exponent 1/2 by means of a nonlinear memoryless transformation applied to a uniform noise. We show that this transformation is expressable in terms of a special function known under the name of the Lambert W function. We review the main methods for numerical evaluation of the relevant branch of the (multivalued) Lambert W function with controlled accuracy and complement them with an original rational function approximation. Based on these methods, synthesis of the generalized Gaussian noise can be performed with arbitrary accuracy. We construct a simple and fast evaluation algorithm with prescribed accuracy, which is especially suited forMonte Carlo simulation requiring large numbers of realizations of the generalized Gaussian noise.
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https://hal.archives-ouvertes.fr/hal-00845481
Contributor : Marie-Françoise Gerard Connect in order to contact the contributor
Submitted on : Thursday, July 18, 2013 - 9:49:25 AM
Last modification on : Wednesday, October 20, 2021 - 3:19:05 AM

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  • HAL Id : hal-00845481, version 1

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François Chapeau-Blondeau, Abdelilah Monir. Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2002, 50, pp.2160-2165. ⟨hal-00845481⟩

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