Given the following statements:Statement 1:A periodic signal cannot be anticausal.Statement 2:An energy signal must be of finite duration.Choose the correct option for the above statements
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Answer & Explanation
Correct AnswerA. Statement 1 is true, but statement 2 is false
Quick Explanation
A nonzero periodic signal repeats indefinitely; if it were zero for all positive time as a purely anticausal signal, periodic repetition would force it to be zero everywhere. An energy signal, however, need not have finite duration—for example an exponentially decaying signal can extend indefinitely yet have finite energy. Hence statement 1 is true and statement 2 false: option A.
Formula / Key Relation
Energy E=∫|x(t)|²dt <∞
Detailed Explanation
Correct Answer
A — Statement 1 is true, but statement 2 is false
Concept and Reasoning
A nonzero periodic signal repeats indefinitely; if it were zero for all positive time as a purely anticausal signal, periodic repetition would force it to be zero everywhere. An energy signal, however, need not have finite duration—for example an exponentially decaying signal can extend indefinitely yet have finite energy. Hence statement 1 is true and statement 2 false: option A.
Calculation / Key Relation
Energy E=∫|x(t)|²dt <∞
Exam Takeaway
Finite energy does not imply finite duration.
Common Mistake
Do not confuse time support with convergence of the energy integral.
Quick Trick
Finite energy does not imply finite duration.
Common Mistake
Do not confuse time support with convergence of the energy integral.
Exam Tip
Finite energy does not imply finite duration.
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