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Which one of the following is the correct statement forThe continuous time system described by y(t) = x(t2)
- a)Causal, linear and time varying
- b)Causal, non - linear and time varying
- c)Non - causal linear, and time variant
- d)Non - causal, non - linear and time invariant
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which one of the following is the correct statement forThe continuous ...
it is linear because it has no square of signal, it is non-causal because input depends on future value.
It does not satisfy two rules so it is time- variable.
It does not satisfy two rules so it is time- variable.
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Which one of the following is the correct statement forThe continuous ...
Understanding the System: y(t) = x(t²)
The system described by the equation y(t) = x(t²) can be analyzed in terms of causality, linearity, and time invariance.
Causality
- A system is causal if the output at any time depends only on present and past inputs, not future inputs.
- In this case, y(t) = x(t²) means that the output at time t depends on the input at time t².
- Since t² can be greater than t (for t > 1), the output can depend on future values of the input.
- Therefore, the system is non-causal.
Linearity
- A system is linear if it satisfies the principles of superposition (additivity and homogeneity).
- Consider two inputs x1(t) and x2(t) leading to outputs y1(t) = x1(t²) and y2(t) = x2(t²).
- If we take a linear combination of inputs, say a*x1(t) + b*x2(t), the output becomes y(t) = x(a*t² + b*t²), which does not correspond to a linear combination of y1(t) and y2(t).
- Thus, the system is non-linear.
Time Invariance
- A system is time-invariant if a time shift in the input results in an equivalent time shift in the output.
- If we shift the input x(t) by t0, the output becomes y(t) = x((t - t0)²), which is not simply y(t - t0).
- Therefore, the system is time-varying.
Conclusion
Based on the analysis:
- Non-causal
- Non-linear
- Time-varying
The correct classification for the continuous-time system y(t) = x(t²) is option D: Non-causal, non-linear, and time invariant.
The system described by the equation y(t) = x(t²) can be analyzed in terms of causality, linearity, and time invariance.
Causality
- A system is causal if the output at any time depends only on present and past inputs, not future inputs.
- In this case, y(t) = x(t²) means that the output at time t depends on the input at time t².
- Since t² can be greater than t (for t > 1), the output can depend on future values of the input.
- Therefore, the system is non-causal.
Linearity
- A system is linear if it satisfies the principles of superposition (additivity and homogeneity).
- Consider two inputs x1(t) and x2(t) leading to outputs y1(t) = x1(t²) and y2(t) = x2(t²).
- If we take a linear combination of inputs, say a*x1(t) + b*x2(t), the output becomes y(t) = x(a*t² + b*t²), which does not correspond to a linear combination of y1(t) and y2(t).
- Thus, the system is non-linear.
Time Invariance
- A system is time-invariant if a time shift in the input results in an equivalent time shift in the output.
- If we shift the input x(t) by t0, the output becomes y(t) = x((t - t0)²), which is not simply y(t - t0).
- Therefore, the system is time-varying.
Conclusion
Based on the analysis:
- Non-causal
- Non-linear
- Time-varying
The correct classification for the continuous-time system y(t) = x(t²) is option D: Non-causal, non-linear, and time invariant.
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Which one of the following is the correct statement forThe continuous time system described by y(t) = x(t2)a) Causal, linear and time varyingb) Causal, non - linear and time varyingc)Non - causal linear, and time variantd) Non - causal, non - linear and time invariantCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Which one of the following is the correct statement forThe continuous time system described by y(t) = x(t2)a) Causal, linear and time varyingb) Causal, non - linear and time varyingc)Non - causal linear, and time variantd) Non - causal, non - linear and time invariantCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is the correct statement forThe continuous time system described by y(t) = x(t2)a) Causal, linear and time varyingb) Causal, non - linear and time varyingc)Non - causal linear, and time variantd) Non - causal, non - linear and time invariantCorrect answer is option 'D'. Can you explain this answer?.
Which one of the following is the correct statement forThe continuous time system described by y(t) = x(t2)a) Causal, linear and time varyingb) Causal, non - linear and time varyingc)Non - causal linear, and time variantd) Non - causal, non - linear and time invariantCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Which one of the following is the correct statement forThe continuous time system described by y(t) = x(t2)a) Causal, linear and time varyingb) Causal, non - linear and time varyingc)Non - causal linear, and time variantd) Non - causal, non - linear and time invariantCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is the correct statement forThe continuous time system described by y(t) = x(t2)a) Causal, linear and time varyingb) Causal, non - linear and time varyingc)Non - causal linear, and time variantd) Non - causal, non - linear and time invariantCorrect answer is option 'D'. Can you explain this answer?.
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