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Comment on the causality of the following discrete time system: y[n] = x[-n].
- a)Causal
- b)Non causal
- c)Both Casual and Non casual
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Comment on the causality of the following discrete time system: y[n] =...
For positive time, the output depends on the input at an earlier time, giving causality for this portion. However, at a negative time, the output depends on the input at a positive time, i.e. at a time in the future, rendering it non causal.
Most Upvoted Answer
Comment on the causality of the following discrete time system: y[n] =...
Explanation:
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. In other words, the output does not depend on future values of the input.
In the given discrete time system, y[n] = x[-n], the output y[n] is determined by the input x[-n]. The negative sign in x[-n] indicates that the input is delayed by n units.
Let's analyze the system to determine its causality.
1. Causal Systems:
- A causal system is one where the output at any given time depends only on the present and past values of the input.
- In a causal system, the output cannot depend on future values of the input.
- For a causal system, the output should be independent of future values of the input.
- In the given system, y[n] = x[-n], the output y[n] depends on the input x[-n], which is a future value of the input.
- Therefore, the given system is not causal.
2. Non-Causal Systems:
- A non-causal system is one where the output at any given time depends on future values of the input.
- In a non-causal system, the output depends on both past and future values of the input.
- In the given system, y[n] = x[-n], the output y[n] depends on the input x[-n], which is a future value of the input.
- Therefore, the given system is non-causal.
Conclusion:
Based on the above analysis, we can conclude that the given discrete time system y[n] = x[-n] is non-causal. The output at any given time depends on future values of the input, which violates the causality condition.
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. In other words, the output does not depend on future values of the input.
In the given discrete time system, y[n] = x[-n], the output y[n] is determined by the input x[-n]. The negative sign in x[-n] indicates that the input is delayed by n units.
Let's analyze the system to determine its causality.
1. Causal Systems:
- A causal system is one where the output at any given time depends only on the present and past values of the input.
- In a causal system, the output cannot depend on future values of the input.
- For a causal system, the output should be independent of future values of the input.
- In the given system, y[n] = x[-n], the output y[n] depends on the input x[-n], which is a future value of the input.
- Therefore, the given system is not causal.
2. Non-Causal Systems:
- A non-causal system is one where the output at any given time depends on future values of the input.
- In a non-causal system, the output depends on both past and future values of the input.
- In the given system, y[n] = x[-n], the output y[n] depends on the input x[-n], which is a future value of the input.
- Therefore, the given system is non-causal.
Conclusion:
Based on the above analysis, we can conclude that the given discrete time system y[n] = x[-n] is non-causal. The output at any given time depends on future values of the input, which violates the causality condition.
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Comment on the causality of the following discrete time system: y[n] = x[-n].a)Causalb)Non causalc)Both Casual and Non casuald)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?
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