A signal f(t) has energy E, the energy of the signal f(2t)

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A signal f(t) has energy E, the energy of the signal f(2t)

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A signal f(t) has energy E, the energy of the signal f(2t) will be energy—

1. E
2. E
  2
3. 2E
4. None of these

Correct Option: B

We know that energy of a signal is given as
E = ∫^∞_–∞ |f(t)|²dt
Consider energy for signal f(2t) is E′
then E′ = ∫^∞_–∞ |f(p)|²dp
Let 2t = p
dt = dp
2

E′ = ∫^∞_–∞ |f(t)|² dt 2

E′ = E
2

(∵ by using change of variable property)
Hence, alternative (B) is the correct choice.