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Comment on the causality of the discrete time system: y[n] = x[n+3].
- a)Causal
- b)Non Causal
- c)Anti Causal
- d)None of the mentioned
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Comment on the causality of the discrete time system: y[n] = x[n+3].a)...
The output always depends on the input at a time in the future, rendering it anti-causal.
Most Upvoted Answer
Comment on the causality of the discrete time system: y[n] = x[n+3].a)...
Definition of Causality
A discrete-time system is said to be causal if its 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.
Explanation
The given system is described by the equation y[n] = x[n-3], where x[n] represents the input and y[n] represents the output.
To determine causality, we need to analyze the relationship between the input and output for different values of n.
Analysis of the System
Let's consider the current time index as n = 0. According to the system equation, the output at this time index is y[0] = x[0-3] = x[-3].
Since the output at n = 0 depends on the input at n = -3, which is a future value, the system is not causal.
Explanation of the Correct Answer
The correct answer is option 'C' (Anti Causal) because the system described by the equation y[n] = x[n-3] is not causal. The output at any given time index depends on future values of the input, violating the causality condition.
Conclusion
In summary, the given discrete-time system y[n] = x[n-3] is anti-causal as it violates the causality condition. The output at any given time index depends on future values of the input.
A discrete-time system is said to be causal if its 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.
Explanation
The given system is described by the equation y[n] = x[n-3], where x[n] represents the input and y[n] represents the output.
To determine causality, we need to analyze the relationship between the input and output for different values of n.
Analysis of the System
Let's consider the current time index as n = 0. According to the system equation, the output at this time index is y[0] = x[0-3] = x[-3].
Since the output at n = 0 depends on the input at n = -3, which is a future value, the system is not causal.
Explanation of the Correct Answer
The correct answer is option 'C' (Anti Causal) because the system described by the equation y[n] = x[n-3] is not causal. The output at any given time index depends on future values of the input, violating the causality condition.
Conclusion
In summary, the given discrete-time system y[n] = x[n-3] is anti-causal as it violates the causality condition. The output at any given time index depends on future values of the input.
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