A filtering method that uses the Wigner distribution to perform signal differentiation is presented in this paper. The method consists of computing the Wigner distribution for a signal, and applying a smooth roll-off filter to it, rather than a sharp cut-off filter which, as correctly argued by the authors, creates oscillations (Gibb’s phenomenon) in the reconstructed signals and its computed derivatives.

Boundary conditions are treated by using Laplacians as filtering boundaries, and by extrapolating the input signal at both ends. They numerically demonstrate the superiority of Laplacian boundaries over Gaussian ones.

The filtering method requires the estimation of a number of signal-dependent parameters. In their experiments, the authors use a ground-truth signal inside an iterative procedure to optimize the parameters of the filter. Their experiments clearly demonstrate the superiority of their approach. In most real signal processing situations, however, there is no ground-truth signal with experimental measurements available, and this obviously sets a limit to the applications of this method.