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 is, the better will be the matching of the magnitude spectrum with that of the original unstable filter.