If all the poles of H(z) are outside the unit circle, then the system ...
Explanation: If all the poles of H(z) are outside an unit circle, it means that the system is neither causal nor BIBO stable.
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If all the poles of H(z) are outside the unit circle, then the system ...
The correct answer to the given question is option 'D' - None of the mentioned.
Explanation:
- The statement states that if all the poles of H(z) are outside the unit circle, then the system is said to have certain properties. Let's analyze these properties and understand why none of the options mentioned are correct.
Causal System:
- A system is said to be causal if the output at any given time depends only on the present and past values of the input. Causality implies that the system does not depend on future values of the input.
- The location of poles in the z-plane does not determine the causality of the system. Therefore, we cannot conclude that the system is only causal based on the given information.
BIBO Stability:
- BIBO stability stands for Bounded-Input Bounded-Output stability. A system is considered to be BIBO stable if every bounded input to the system produces a bounded output. In other words, if the input to the system is bounded, the output should also be bounded.
- The location of poles in the z-plane does affect the stability of the system. If all the poles of H(z) are outside the unit circle, then the system is stable in the sense that it will not exhibit exponential growth or oscillations in response to bounded inputs. However, this information alone does not guarantee that the system is BIBO stable.
- BIBO stability also depends on the location of zeros in the z-plane. If there are any zeros inside or on the unit circle, the system may still exhibit unbounded behavior for certain inputs.
- Therefore, we cannot conclude that the system is only BIBO stable based on the given information.
Conclusion:
- Based on the above analysis, we can conclude that none of the mentioned options (a, b, c) are correct. The given information about the poles being outside the unit circle does not provide enough information to determine the causality or BIBO stability of the system. Additional information about the zeros and other properties of the system would be required to make any definitive conclusions.