The unit circle

What is the meaning of a pole? We will see that the location of poles determines whether filters are stable (have finite output) or unstable (have unbounded output). Considering both positive and negative values of $\rho$,we find that stability is associated with $\vert\rho \vert<1$.The pole $\vert\rho \vert<1$happens to be real, but we will soon see that poles are complex more often than not. In the case of complex poles, the condition of stability is that they all should satisfy |Z_p|>1. In the complex Z-plane, this means that all the poles should be outside a circle of unit radius, the so-called unit circle.