On the proof of stabilization of two-dimensional recursive filters via discrete Hilbert transform

In this paper, we prove that the two-dimensional recursive digital filters stabilized via the discrete Hilbert transform (DHT) would be stable, with a constraint on the amplitude of the frequency spectrum of the original unstable filter. It is pointed out in the discussion that the finer the grid
(w_1, w_2)
is, the better will be the matching of the magnitude spectrum with that of the original unstable filter.