To understand such behavior of pure wsLSSA, we can re-late to the Nyquist-Shannon-Kotelnikov resolution/maximal frequency conditions in the DFT (see Sec. II B and II D). For a set of points in s-space with increment ∆s (s i = i•∆s), the maximal frequency in the DFT will be given as 2π/∆s. However, due to the sM(s) curve being real-valued and due to the oddness of the sine-FT , the unique part of RDF will be limited by half of this value. Thus, our maximal resolvable distance is r max = π/∆s. In our case r max = π/0.2 = 16 Å, exceeding our maximal value max({r k } M k=1 ) = 4 Å. As for the minimal increment in r-space, the DFT-condition is ∆r = 2π/s max , which in our case is ∆r = 2π/32 = 0.198. For M = 16, we get the increment ∆r = 0.200, which exceeds this limit. For M = 17, we get ∆r = 0.187, which is smaller than this limit. Therefore, it seems like we can estimate the applicability of the unregularized wsLSSA routine using simple DFT-based relations. The maximal r should not exceed the r max = π/∆s, where ∆s is the mean increment for the experimental data. And the increment for the points in r-space should be larger than ∆r min = 2π/ max {s i } N i=1 , where max {s i } N i=1 is the value in a set {s i } N i=1 . As an example of the regularization, we have taken the dataset with the same range of r (1 ≤ r ≤ 4 Å) but increased the number of equally-spaced points to M = 50, M = 100, and M = 150. For these sets of r-points, the regularization parameter α was scanned in the range 10 -7 ≤ α ≤ 10 2 to apply the L-curve criterion (see Sec. II E). The resulting L-curves are shown in Fig. . The corners of the curves in all our cases appear at a value of α L-curve = 5 × 10 -4 . If we apply the criterion from Eq. 26, we get α opt equal to α opt = 0.0004 for M = 50, α opt = 0.0008 for M = 100, and α opt = 0.0012 for M = 150, which are reasonably close to that value from the L-curve criterion (Fig. ).