Final answer:
A minimum-phase system requires that all poles and zeros be inside the unit circle in the z-plane to ensure causality and stability for both the system and its inverse.
Step-by-step explanation:
The question relates to the constraints on the poles and zeros of the system function of a minimum-phase system in the z-plane. A minimum-phase system must be causal and stable, and its inverse must also have these properties. For the system to be causal, all of its poles and zeros must lie within the unit circle in the z-plane, since causal systems depend only on past and present inputs, not future ones.
Stability requires that all poles must be inside the unit circle; if any pole lies on or outside the unit circle, the system will exhibit an unstable response. However, zeros can lie anywhere in the z-plane and still allow the system to be stable; for a minimum-phase system, the zeros must also be inside the unit circle to ensure that the inverse is causal and stable. Therefore, the necessary constraints for a minimum-phase system are that all poles and zeros must be located inside the unit circle in the z-plane.