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The system having input x (n) related to output y(n) as y (n) = log |x (n)| is:
- a)Nonlinear, causal, stable
- b)Linear, noncausal, stable
- c)Nonlinear, causal, not stable
- d)Linear, noncausal, not stable
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The system having input x (n) related to output y(n) as y (n) = log |x...
Explanation: As y (n) is the function of x (n) hence it is nonlinear but it is bounded and also depends upon past and present values therefore it is stable and causal respectively.
Most Upvoted Answer
The system having input x (n) related to output y(n) as y (n) = log |x...
Explanation:
The given system has input x(n) and output y(n), which is related as y(n) = log |x(n)|. Let's analyze the system characteristics based on the given relation.
Nonlinear:
- A system is linear if it satisfies the properties of superposition and homogeneity.
- Superposition property states that the response of a system to a sum of inputs is equal to the sum of individual responses to each input.
- Homogeneity property states that the response of a system to a scaled input is equal to the same scale factor applied to the response of the original input.
- In this case, if we apply the superposition property, y(n) = log |a*x1(n) + b*x2(n)|, where a and b are constants and x1(n) and x2(n) are two inputs.
- However, we cannot simplify this equation using the homogeneity property as log |a*x1(n) + b*x2(n)| is not equal to a*log |x1(n)| + b*log |x2(n)|.
- Therefore, the given system is nonlinear.
Causal:
- A system is causal if the output depends only on present and past inputs, not future inputs.
- In this case, the output y(n) depends only on the present and past value of the input x(n), not future values.
- Therefore, the given system is causal.
Stable:
- A system is stable if a bounded input produces a bounded output.
- In this case, we can see that the output y(n) is always a positive number because of the absolute value function.
- Therefore, the output y(n) is always bounded for any bounded input x(n).
- Therefore, the given system is stable.
Conclusion:
- Based on the above analysis, we can conclude that the given system is nonlinear, causal, and stable.
- Therefore, option 'A' is the correct answer.
The given system has input x(n) and output y(n), which is related as y(n) = log |x(n)|. Let's analyze the system characteristics based on the given relation.
Nonlinear:
- A system is linear if it satisfies the properties of superposition and homogeneity.
- Superposition property states that the response of a system to a sum of inputs is equal to the sum of individual responses to each input.
- Homogeneity property states that the response of a system to a scaled input is equal to the same scale factor applied to the response of the original input.
- In this case, if we apply the superposition property, y(n) = log |a*x1(n) + b*x2(n)|, where a and b are constants and x1(n) and x2(n) are two inputs.
- However, we cannot simplify this equation using the homogeneity property as log |a*x1(n) + b*x2(n)| is not equal to a*log |x1(n)| + b*log |x2(n)|.
- Therefore, the given system is nonlinear.
Causal:
- A system is causal if the output depends only on present and past inputs, not future inputs.
- In this case, the output y(n) depends only on the present and past value of the input x(n), not future values.
- Therefore, the given system is causal.
Stable:
- A system is stable if a bounded input produces a bounded output.
- In this case, we can see that the output y(n) is always a positive number because of the absolute value function.
- Therefore, the output y(n) is always bounded for any bounded input x(n).
- Therefore, the given system is stable.
Conclusion:
- Based on the above analysis, we can conclude that the given system is nonlinear, causal, and stable.
- Therefore, option 'A' is the correct answer.
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The system having input x (n) related to output y(n) as y (n) = log |x...
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