Series of cosine (left) and box spline (right) filters for a cubic periodic domain of size N = 512 pixels. Their total sum is indicated as well as the wavenumber boundaries for a 3D domain (k_min = 1, $k_{\max }=\sqrt{3}N/2$). Colours from red to blue stand for filter indices 0 to J. This figure illustrates how many filters are necessary in order for the reconstruction formula to be valid. In practice however, diffusion damps the higher k end of the spectrum, and convergence is reached for a slightly lower number of filters.