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A minimum phase system has all zeros1 pointAll of the aboveoutside of the unit circle in z-planeinside of the unit circle in z-planeSome inside and some outside of the unit circle in z-plane

Question

A minimum phase system has all zeros1 pointAll of the aboveoutside of the unit circle in z-planeinside of the unit circle in z-planeSome inside and some outside of the unit circle in z-plane

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Solution

A minimum phase system has all zeros inside of the unit circle in z-plane.

Here's why:

  1. A system is said to be minimum phase if its transfer function has all its zeros and poles inside the unit circle in the z-plane.

  2. The unit circle in the z-plane is a circle of radius 1 centered at the origin.

  3. If a zero is inside the unit circle, it means that its magnitude is less than 1.

  4. Therefore, a minimum phase system has all its zeros with magnitude less than 1, i.e., inside the unit circle in the z-plane.

  5. If a zero is outside the unit circle, its magnitude is greater than 1, and the system is not minimum phase.

  6. If some zeros are inside and some are outside the unit circle, the system is also not minimum phase.

So, the correct answer is "inside of the unit circle in z-plane".

This problem has been solved

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