We saw in §8.4 that an LTI filter is stable if and only if all of its poles are strictly inside the unit circle ( ) in the complex plane. In particular, a pole outside the unit circle ( ) gives rise to an impulse-response component proportional to which grows exponentially over time . We also saw in §6.2 that the z transform of a growing exponential does not converge on the unit circle in the plane. However, this was the case for a causal exponential , where is the unit-step function (which switches from 0 to 1 at time 0). If the same exponential is instead anticausal, i.e., of the form , then, as we'll see in this section, its z transform does exist on the unit circle, and the pole is in exactly the same place as in the causal case. Therefore,to unambiguously invert a z transform, we must know its region of convergence. The critical question is whether the region of convergence includes the unit circle: If it does, then each pole outside the unit circle corresponds to an anticausal, finite energy, exponential, while each pole inside corresponds to the usual causal decaying exponential.