Discussion
Which quantity is preserved by an ideal transform between time and frequency?
Answer: B
Energy is preserved, which is the content of Parseval's relation and the reason a spectrum can be used to compute power. Bandwidth and duration are not preserved in any sense; they trade against one another. Peak amplitude in one domain bears no simple relation to the peak in the other, as the impulse and its flat spectrum show most starkly. Energy conservation is what makes the two representations genuinely equivalent rather than merely related.
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