GATE EC 2023 Set 1 — Question 27
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Signals & Systems → Continuous-Time Signals → Energy & Power Signals
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Question
Let be a strictly band-limited signal with bandwidth and energy . Assuming , the energy in the signal is
Correct answer
(B) (E)/(2)
Solution
The energy of a signal is defined as .Let . The energy of is:Using the trigonometric identity :The first term is , where is the energy of .For the second term, let . If is band-limited to , then is band-limited to . The integral represents the real part of the Fourier transform of evaluated at frequency .Given , the frequency . Since the signal is band-limited to and , its spectral component at is zero. Therefore:Thus, the total energy is:Hence, option (B) is correct.
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