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
Solution
A minimum phase system has all zeros inside of the unit circle in z-plane.
Here's why:
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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.
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The unit circle in the z-plane is a circle of radius 1 centered at the origin.
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If a zero is inside the unit circle, it means that its magnitude is less than 1.
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Therefore, a minimum phase system has all its zeros with magnitude less than 1, i.e., inside the unit circle in the z-plane.
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If a zero is outside the unit circle, its magnitude is greater than 1, and the system is not minimum phase.
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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".
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