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H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable its
- a)Poles must be inside the unit circle and zeros must be outside the unit circle.
- b)Poles and zeros must be inside the unit circle.
- c)Poles and zeros must be outside the unit circle.
- d)Poles must be outside the unit circle and the zeros should be inside the unit circle.
Correct answer is option 'B'. Can you explain this answer?
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H(z) is discrete rational transfer function. To ensure that both H(z) ...
For H(z) to be stable the poles of H(z) must be inside the unit circle.
For the inverse of H(z) to be stable the poles inverse of H(z) must be inside the unit circle.
The poles of inverse of H(z) are the zeros of H(z)
Hence, both poles and zeros of H(z) must be inside the unit circle.
Most Upvoted Answer
H(z) is discrete rational transfer function. To ensure that both H(z) ...
Stability of a Discrete Rational Transfer Function
A discrete rational transfer function H(z) is a mathematical representation of a discrete-time system in the z-domain. The stability of H(z) is an important consideration in control systems and signal processing applications. In order for both H(z) and its inverse to be stable, certain conditions must be met.
Poles and Zeros
Poles and zeros are the key elements of a transfer function. Poles represent the values of z for which the transfer function becomes infinite or undefined, while zeros represent the values of z for which the transfer function becomes zero. The locations of the poles and zeros in the z-plane determine the stability of the system.
Unit Circle
The unit circle in the z-plane is a circle with a radius of 1, centered at the origin. It is commonly used as a reference for stability analysis in discrete-time systems. The unit circle divides the z-plane into two regions: the interior of the circle and the exterior of the circle.
Stability Conditions
To ensure that both H(z) and its inverse are stable, the following conditions must be met:
1. Poles inside the unit circle: The poles of H(z) must lie inside the unit circle. Poles outside the unit circle indicate an unstable system, as they can cause the output to grow exponentially over time.
2. Zeros outside the unit circle: The zeros of H(z) must lie outside the unit circle. Zeros inside the unit circle can result in unstable behavior, as they can cause the output to oscillate or diverge.
Explanation of Answer
The correct answer is option 'B', which states that both the poles and zeros of H(z) must be inside the unit circle. This answer is supported by the stability conditions mentioned above.
If the poles of H(z) are inside the unit circle, it ensures that the system is stable and the output remains bounded. If the poles were outside the unit circle, the system would be unstable and the output would grow exponentially over time.
Similarly, if the zeros of H(z) are outside the unit circle, it ensures that the system is stable and the output does not oscillate or diverge. If the zeros were inside the unit circle, the system could exhibit unstable behavior.
Therefore, both conditions must be satisfied for H(z) and its inverse to be stable. Poles inside the unit circle and zeros outside the unit circle ensure stable behavior and bounded output.
In conclusion, the correct answer is option 'B' - Poles and zeros must be inside the unit circle.
A discrete rational transfer function H(z) is a mathematical representation of a discrete-time system in the z-domain. The stability of H(z) is an important consideration in control systems and signal processing applications. In order for both H(z) and its inverse to be stable, certain conditions must be met.
Poles and Zeros
Poles and zeros are the key elements of a transfer function. Poles represent the values of z for which the transfer function becomes infinite or undefined, while zeros represent the values of z for which the transfer function becomes zero. The locations of the poles and zeros in the z-plane determine the stability of the system.
Unit Circle
The unit circle in the z-plane is a circle with a radius of 1, centered at the origin. It is commonly used as a reference for stability analysis in discrete-time systems. The unit circle divides the z-plane into two regions: the interior of the circle and the exterior of the circle.
Stability Conditions
To ensure that both H(z) and its inverse are stable, the following conditions must be met:
1. Poles inside the unit circle: The poles of H(z) must lie inside the unit circle. Poles outside the unit circle indicate an unstable system, as they can cause the output to grow exponentially over time.
2. Zeros outside the unit circle: The zeros of H(z) must lie outside the unit circle. Zeros inside the unit circle can result in unstable behavior, as they can cause the output to oscillate or diverge.
Explanation of Answer
The correct answer is option 'B', which states that both the poles and zeros of H(z) must be inside the unit circle. This answer is supported by the stability conditions mentioned above.
If the poles of H(z) are inside the unit circle, it ensures that the system is stable and the output remains bounded. If the poles were outside the unit circle, the system would be unstable and the output would grow exponentially over time.
Similarly, if the zeros of H(z) are outside the unit circle, it ensures that the system is stable and the output does not oscillate or diverge. If the zeros were inside the unit circle, the system could exhibit unstable behavior.
Therefore, both conditions must be satisfied for H(z) and its inverse to be stable. Poles inside the unit circle and zeros outside the unit circle ensure stable behavior and bounded output.
In conclusion, the correct answer is option 'B' - Poles and zeros must be inside the unit circle.
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H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable itsa)Poles must be inside the unit circle and zeros must be outside the unit circle.b)Poles and zeros must be inside the unit circle.c)Poles and zeros must be outside the unit circle.d)Poles must be outside the unit circle and the zeros should be inside the unit circle.Correct answer is option 'B'. Can you explain this answer?
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H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable itsa)Poles must be inside the unit circle and zeros must be outside the unit circle.b)Poles and zeros must be inside the unit circle.c)Poles and zeros must be outside the unit circle.d)Poles must be outside the unit circle and the zeros should be inside the unit circle.Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable itsa)Poles must be inside the unit circle and zeros must be outside the unit circle.b)Poles and zeros must be inside the unit circle.c)Poles and zeros must be outside the unit circle.d)Poles must be outside the unit circle and the zeros should be inside the unit circle.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable itsa)Poles must be inside the unit circle and zeros must be outside the unit circle.b)Poles and zeros must be inside the unit circle.c)Poles and zeros must be outside the unit circle.d)Poles must be outside the unit circle and the zeros should be inside the unit circle.Correct answer is option 'B'. Can you explain this answer?.
H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable itsa)Poles must be inside the unit circle and zeros must be outside the unit circle.b)Poles and zeros must be inside the unit circle.c)Poles and zeros must be outside the unit circle.d)Poles must be outside the unit circle and the zeros should be inside the unit circle.Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable itsa)Poles must be inside the unit circle and zeros must be outside the unit circle.b)Poles and zeros must be inside the unit circle.c)Poles and zeros must be outside the unit circle.d)Poles must be outside the unit circle and the zeros should be inside the unit circle.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for H(z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable itsa)Poles must be inside the unit circle and zeros must be outside the unit circle.b)Poles and zeros must be inside the unit circle.c)Poles and zeros must be outside the unit circle.d)Poles must be outside the unit circle and the zeros should be inside the unit circle.Correct answer is option 'B'. Can you explain this answer?.
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