An LTI system is minimum phase if

Explanation:

Minimum Phase LTI System

Definition: A Linear Time-Invariant (LTI) system is considered to be a minimum phase system if all its poles and zeros are located within the unit circle in the Z-plane. The unit circle is defined as the set of points in the complex plane where the magnitude of the complex number is equal to 1. For a minimum phase system, both stability and minimum phase conditions are satisfied.

Key Characteristics of a Minimum Phase System:

• All poles of the system must lie strictly inside the unit circle. This ensures the system is stable.
• All zeros of the system must also lie strictly inside the unit circle. This ensures the system has the minimum phase property.
• The system's phase response is minimized, which is crucial in many control and signal processing applications where phase linearity or minimal phase shift is required.

Explanation of the Correct Option:

The correct option is:

Option 4: All poles and zeros are inside the unit circle.

This is the correct condition for a minimum phase LTI system. For a system to be classified as minimum phase, it is not sufficient for just the poles or just the zeros to be inside the unit circle—both must satisfy this condition. This ensures that the system is stable and has the minimum phase property.