If the energy of a signal x[n] is E, then the energy of the signal x[m – n], where m is an integer, is
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Answer & Explanation
Correct AnswerA. E
Quick Explanation
The transformation x[m−n] is a reversal of the sample order followed by a shift. Neither operation changes the set of squared magnitudes being summed, so signal energy remains E. Hence option A is correct.
Formula / Key Relation
E=Σ|x[n]|²=Σ|x[m−n]|²
Detailed Explanation
Correct Answer
A — E
Concept and Reasoning
The transformation x[m−n] is a reversal of the sample order followed by a shift. Neither operation changes the set of squared magnitudes being summed, so signal energy remains E. Hence option A is correct.
Calculation / Key Relation
E=Σ|x[n]|²=Σ|x[m−n]|²
Exam Takeaway
Shift and time reversal preserve energy.
Common Mistake
Do not multiply energy by the shift index m; m changes sample location, not amplitude.
Quick Trick
Shift and time reversal preserve energy.
Common Mistake
Do not multiply energy by the shift index m; m changes sample location, not amplitude.
Exam Tip
Shift and time reversal preserve energy.
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