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 ofz=r for which hn]" is absolutely summable Thus if the roc includes the unit circle 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 − [ ]