Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2 - Archive ouverte HAL Access content directly
Journal Articles IEEE Transactions on Signal Processing Year : 2002

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.
No file

Dates and versions

hal-00845481 , version 1 (18-07-2013)

Identifiers

  • HAL Id : hal-00845481 , version 1

Cite

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, 2002, 50, pp.2160-2165. ⟨hal-00845481⟩

Collections

UNIV-ANGERS
61 View
0 Download

Share

Gmail Facebook X LinkedIn More