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The system described by the input-output equations y(n)=x2(n) is a Non-linear system.
- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The system described by the input-output equations y(n)=x2(n) is a Non...
Explanation: Given equation is y(n)=x2(n)
Let y1(n)=x12(n) and y2(n)=x22(n)
y3(n)=y1(n)+y2(n)= x12(n)+ x22(n)≠(x1(n)+x2(n))2
So the system is non-linear.
Let y1(n)=x12(n) and y2(n)=x22(n)
y3(n)=y1(n)+y2(n)= x12(n)+ x22(n)≠(x1(n)+x2(n))2
So the system is non-linear.
Most Upvoted Answer
The system described by the input-output equations y(n)=x2(n) is a Non...
Non-linear System
A non-linear system is a system whose output is not directly proportional to the input. In other words, the system is not linear. The input-output equation y(n)=x2(n) represents a system whose output is the square of the input. This system is not linear because the output is not directly proportional to the input. If we double the input, the output does not double. Therefore, the correct answer is option A.
Explanation
To understand why the system described by the input-output equation y(n)=x2(n) is non-linear, let us consider an example. Suppose the input to the system is x(n) = 2. Then the output of the system is y(n) = 22 = 4. Now, let us double the input to x(n) = 4. The output of the system is y(n) = 42 = 16. The output has quadrupled, not doubled. This shows that the system is not linear because the output is not directly proportional to the input.
Conclusion
In conclusion, the input-output equation y(n)=x2(n) represents a non-linear system because the output is not directly proportional to the input. If we double the input, the output does not double. Therefore, the correct answer is option A.
A non-linear system is a system whose output is not directly proportional to the input. In other words, the system is not linear. The input-output equation y(n)=x2(n) represents a system whose output is the square of the input. This system is not linear because the output is not directly proportional to the input. If we double the input, the output does not double. Therefore, the correct answer is option A.
Explanation
To understand why the system described by the input-output equation y(n)=x2(n) is non-linear, let us consider an example. Suppose the input to the system is x(n) = 2. Then the output of the system is y(n) = 22 = 4. Now, let us double the input to x(n) = 4. The output of the system is y(n) = 42 = 16. The output has quadrupled, not doubled. This shows that the system is not linear because the output is not directly proportional to the input.
Conclusion
In conclusion, the input-output equation y(n)=x2(n) represents a non-linear system because the output is not directly proportional to the input. If we double the input, the output does not double. Therefore, the correct answer is option A.
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