Stability Condition in Terms of the pole locations The roc of the z-transform H(z)of the impulse response sequence hn] is defined by values of z-r for which hin]r"is absolutely summable Thus, if the roc includes the unit circle z 1. then the digital filter is stable and vice versa Copyright C 2001, S K. MitraCopyright © 2001, S. K. Mitra 2 Stability Condition in Terms of the Pole Locations • The ROC of the z-transform H(z) of the impulse response sequence h[n] is defined by values of |z| = r for which is absolutely summable • Thus, if the ROC includes the unit circle |z| = 1, then the digital filter is stable, and vice versa n h n r − [ ]