Stabilization of 2-D recursive digital filters by the DHT method

In this paper, we discuss the discrete Hilbert transform (DHT) method of stabilizing unstable two-dimensional (2-D) recursive digital filters originally proposed by Read and Treitel (se IEEE Trans. Geo. Sci. Electron., vol. GE-II, p. 153-60, 207, July 1973). We show that even in the one-dimensional case, the DHT method may yield an unstable polynomial when the given unstable polynomial has zeros on the unit circle. This is the case in the example presented by Read and Treitel, where the given 2-D polynomial has zeros on the unit bicircle. We show that the DHT method cannot guarantee stability if the unstable 2-D polynomial has zeros on the unit bicircle.