alleryStart learning →Parseval's theorem for the continuous-time Fourier transform states which?
A∫x(t) dt = X(0) holds only for purely real signals
B∫|x(t)|² dt = (1/2π) ∫|X(jω)|² dω (energy ok)
C∫x(t)·u(t) dt = X(∞) is finite under any conditions
D∫x(t)² dt is identically zero for all valid signals
Answer & Solution
Correct answer: B. ∫|x(t)|² dt = (1/2π) ∫|X(jω)|² dω (energy ok)
Parseval (Oppenheim Ch.4): the L² norm in time equals (1/2π) × L² norm in frequency.
Energy is invariant under Fourier transform. Used in BER analysis.
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