• For the stability of the LTI system, the unit-sample response should decay to zero as A necessary and sufficient condition for the stability of a discrete-time LTI system is that all its poles lie strictly inside the unit circle.

• A discrete-time LTI system is called a minimum- phase system if all its poles and zeros lie inside the unit circle. A minimum-phase system is always stable as its poles lie inside the unit circle. Because the zeros of the system lie inside the unit circle, the inverse system with a transfer function   will have all its poles inside the unit circle and be stable.

  •  A discrete-time LTI system is called a maximum- phase system if all its poles and zeros lie outside the unit circle.

Response of a discrete-time LTI system to WSS input

       Consider a discrete-time linear time-invariant system with impulse response and input as shown in Figure 3 below. Assume to be a WSS process with mean and autocorrelation function

Figure 3