If [f(t)] = F(s), then [f(t – T)] is equal to

Home » Signals and Systems » Signal and systems miscellaneous » Question

If [f(t)] = F(s), then [f(t – T)] is equal to—

1. e^sTF(s)
2. e^{– sT}F(s)
3. F(s)
  1 + e^sT
4. F(s)
  1 – e^sT

Correct Option: B

Given that,
if f(t) = F(s)
Then Fourier transform of f(t – T) can be obtained by using time shifting property.
F(t – T) = ∫^∞_–∞f(t – T)e^{– jωt} ·dt
Putting, x = t – T
⇒ t = x + T
dx = dt
= ∫^∞_–∞ f(x)e^{– jω(x + T)}dx
= e^{– jωT} ∫^∞_–∞ f(x).e^{– jωx}dx
= e^{– jωT} F.(s)
= e^{– sT} F.(s)
Hence, alternative (B) is the correct choice.