a) Bi-dimensional Fourier spectra of one of our simulation at different scales. Upper-left: mean of the squared-amplitude of the Fourier coefficients for all patches i.e. . An isotropic un-decimated wavelet transform (“a trous”, see e.g. Starck & Murtagh 2010) is applied to the image and the results for scale one and two are shown in the bottom plots. The upper-right one corresponds to the smooth component. One notices a clear leakage along the null axes. b) Same spectra but working on the prewhitened map and applying a Kaiser-Bessel K_0.5 window function. The leakage along the null axis has clearly disappeared.