The Stabilization of Two-Dimensional Recursive Filters via the Discrete Hilbert Transform

Two-dimensional recursive filters are useful only if stable, that is, if their outputs remain bounded for bounded inputs. The stability of a recursive filter depends on the phase spectrum of its denominator array. A two-dimensional generalization of the discrete Hilbert transform leads to a scheme producing stability with nominal distortions of the filter's desired amplitude spectrum. The method is therefore an attractive alternate to a least-squares procedure recently described by Shanks et al.