abstract: We develop a novel efficient simulation-based procedure to sample from a multivariate distribution when only its characteristic function is known, as often happens in financial applications. To achieve this goal, we combine two strands of the statistical literature: The first one is concerned with the approximation of the density ratio of the original target to an auxiliary measure by orthonormal polynomial series in weighted L2 spaces, the second relates to simulationbased methods where the target density is not available and thus an approximation is used.)